Etydhv

I'd probably lean towards something like aquaponics, a combination of hydroponic (or possibly aeroponic) plant farming with fish or crustacean aquaculture to give you a bit of protein and the plants a bit of fertiliser (by way of the fish poop).

When you're not tied to a conventional growth substrate, you can put your farms up all over the place, such as on the sides and tops of skyscrapers. It'll probably do the microclimate of the city of a world of good, too. The big problem at the moment is growing decent crops... leafy salads are easy, but what you really want is to do is fruits and vegetables and grains and so on. Clearing this technical hurdle doesn't obviously require super future ultratech, so it seems like it fits your needs.

I seem to recall that some existing scifi settings use this sort of setup... I think Gibson's sprawl trilogy references this way of farming, but I'm sure it appears elsewhere too.

You might consider recycling human waste to use as fertiliser but humans have an irritating tendency to use an awful lot of potentially quite hazardous pharmaceuticals and also tend to excrete quite a lot of unpleasant pathogens as well. Treating humanure so that it is safe without also removing its useful properties might be quite challenging. Have a look at the issues with milorganite, as well... it contains concerning levels of heavy metals so it is great for fertilising non-food plants but not so good if you're going to eat the end result. Poop purification may a scifi-step too far for you, but do bear it in mind.

For an even longer shot, consider farming seaweed and shellfish. You'd want the sea to be pretty clean for that sort of thing, but if you're ecologically minded enough to make cities self-sufficient and you're recycling all the poop you're producing, there is hope you can also sort out your polluting industries, too. New York has a lot of coastline, and whilst farming fish tends to be quite polluting, farming shellfish tends to make the sea a nicer place. You might do something like long line mussel farming, perhaps with floating seaweed racks above it. You can always use the mussels to help clean the water for future farming use, and the seaweed for biofuel, until the sea is one day clean enough to eat from again.

Good old Asimov, in his "The caves of steel", used engineered yeasts to feed the megalopolis crowding the under surface of planet Earth.

Normal yeast can be already used as food supplement:

Yeast is used in nutritional supplements, especially those marketed to vegans. It is often referred to as "nutritional yeast" when sold as a dietary supplement. Nutritional yeast is a deactivated yeast, usually S. cerevisiae. It is naturally low in fat and sodium as well as an excellent source of protein and vitamins, especially most B-complex vitamins (contrary to some claims, it contains little or no vitamin B12), as well as other minerals and cofactors required for growth. Some brands of nutritional yeast, though not all, are fortified with vitamin B12, which is produced separately by bacteria.

In 1920, the Fleischmann Yeast Company began to promote yeast cakes in a "Yeast for Health" campaign. They initially emphasized yeast as a source of vitamins, good for skin and digestion. Their later advertising claimed a much broader range of health benefits, and was censured as misleading by the Federal Trade Commission. The fad for yeast cakes lasted until the late 1930s.

Nutritional yeast has a nutty, cheesy flavor and is often used as an ingredient in cheese substitutes. Another popular use is as a topping for popcorn. It can also be used in mashed and fried potatoes, as well as in scrambled eggs. It comes in the form of flakes, or as a yellow powder similar in texture to cornmeal. In Australia, it is sometimes sold as "savoury yeast flakes". Though "nutritional yeast" usually refers to commercial products, inadequately fed prisoners have used "home-grown" yeast to prevent vitamin deficiency.

With some genetic engineering one can overcome the shortcomings.

What you're basically describing is called 'closed loop agriculture'. The idea is that you're capturing all the waste products from creating AND consuming food and recycling them back into the system. Matt Damon's potatoes from 'The Martian' are a perfect example. You're envisioning something on a much larger scale, but the principle in the same.

There are two really critical components to making this idea work for heavily urbanized place.

First: You need to be VERY rigorous in your recycling program. Nothing gets dumped in the Hudson, every bit of water and organic waste your population generates needs to be captured, processed, and cycled back into your food production.

Second: You'd still need a lot of space devoted to food production. Hydroponics and so forth give you ways to concentrate that space, but it only goes so far. This previous article right here from Worldbulding gives some great information on that topic.

I believe there is a concept of vertical farming, in which skyscraper like buildings would have farms on each floor instead of offices.

Using hydroponics or aeroponics a lot more food could be grown per unit of surface area than in traditional dirt farming, and vertical farming would multiply the surface area available for food production in a city. Combining those two should make it possible to grow enough food in a metropolitan area to feed its population.

In a base on an alien planet or a space habitat everything, including wastes, would be recycled. So each atom of carbon, hydrogen, oxygen, nitrogen, etc., would be used over and over again to produce food. And it would certainly be possible to do the same in a city on Earth.

There have been a few questions here about the greatest possible production of food per unit of land surface using various techniques.

See here: Giving Tolkien Architecture a Reality Check: Dwarvish Kingdoms1

and here: How can Dwarves produce honey underground?2

And here: How many people can you feed per square-kilometer of farmland?3

You'll want to start with technology that produces light suitable for growing crops indoors. Grow lights exist of course but they're awfully energy intensive. With near-future technology you'll have better small scale energy sources.

Imagine skyscrapers covered not with a veneer of bricks but rather with solar panels that look like bricks (or stone or siding). We already have solar panels that look like (and take the place of) roofing shingles (with the added bonus that they are each small so any shadow would not take out a whole panel...solar only produces as much as any given cell produces, per panel).

Imagine wind power solutions that do not make noise or harm birds and that are cheap enough to put on every balcony railing and rooftop edge. On every highway/road overpass, or anyplace wind is an issue (cities currently use sculptures and landscaping to deflect wind). Use wave power along the coast as well.

These technologies all exist right now but aren't being produced (much) due to economies of scale, lack of integration with government choices, and so forth. It's all quite doable, with the will to do it. In the near-future, these generators will be more efficient and charge better batteries too. Or so we can imagine.

Use this cheap and easy to access power for (more efficient) grow lights, water pumping (both directions), and ventilation. Now turn walls and hanging room dividers into gardens.

Both in homes:

(Français : Mur végétal Intérieur de l'entreprise Urban Garden)

And in public spaces:

(ref)

For protein and extra fats, grow seeds such as hemp, poppy, mustard, flax, and chia. For calories, hydroponic potatoes, sweet potatoes, for calories plus protein: legumes.

Espaliered fruit trees and vines can be grown against walls with ease. Perhaps a stand on a balcony then have the tree reach up almost to the balcony above. This would give it full sun (if not north facing) and some rainwater. Apple, pear, cherry, grape, fig, citrus, etc (choose for climate).

For even more protein, have some cricket farms.

You'll still need to do some more conventional farming (and animal husbandry) in the parks and rooftops and other open spaces, but these techniques will reduce the amount of space you need for those. You'll also want to choose your landscaping trees and other plants to be edible. Why put in a flowering cherry when you and have a fruiting one?

Starfish Prime has it right with aquaponics. Plenty of room in NYC and other coastal metropolises for that. If you assume that the near future has cleaned up the water.

I'm not sure what the growth medium requires but Cultured Meat and cellular agriculture is becoming more viable each year. It's only a matter of time before the processes are improved to the point that higher volumes could be cultured.

Pass a law that every building over "x" (3-5) stories has to be built with the outer 15' leased to a farm. The buildings are already temperature controlled and have water in them. Executives lose their view of the city for a view through a farm to the city with a glass wall separating the corporate workers from the farm. The farm environment will be completely self contained so crops needing special seasons and temperatures can all be accommodated. Each corporation will need to partner with a farm on building expansions.

Every skyscraper built also contributes to the food production for the city. In conjunction with other ideas presented in other answers this could significantly increase food production.

If you're willing to accept nanotechnology "magic" as an answer, then Feed (or later, Seed) technology as shown in Neal Stephenson's "Diamond Age" can do it. The premises are :

1 ) Nanotech building techniques allow you to create diamond shapes from pure carbon input. Shapes and mixtures of all other elements and compounds can be made given time, energy, templates for the building plans, computation, and other infrastructure considerations.

2 ) Perfect decomposition of garbage, sewage, and random seawater into perfectly segregated elemental lumps. For dangerous elements like fluorine, combine them into safe compounds. A sphere of diamond is probably the safest, most reliable carrying container.

3 ) Perfect pumping system of these lumps. Use spheres instead of cubes, for better pumping. Use pure, clean water as the carrying medium and heat sink. Tag each sphere with its payload lump, track it, and send it out from the decomposition center. Or, have a bunch of decomposition centers and use a system like TCP/IP to send lumps where needed. Either way, it looks like a vascular system pumping out in a Feed.

4 ) Matter compilers in every home, business, and street corner. These request data, power, and lumps of atoms from the Feed. The matter compiler builds physical objects according to the templates in memory or that it fetches from the Internet.

5 ) Each home, business, and street corner has a waste system. If the decomposition machines can be made small, then just have one in every home. If you need a big one, then have a traditional sewage system, which flushes every away to the decomposition machine.

6 ) Power generation from nuclear, geothermal, solar, wind, and/or other sources. Perfect decomposition can also be applied to mining, or seawater, so Uranium is easy to get and refine.

In this city, the population can be extremely dense, only limited by the heat generation of the machinery and people. If people decompose and compile the same atoms with minimal movement every day (food, drink, and clothes can be created from the same atoms discarded as waste earlier in the same building or even room) , then there's relatively little waste from transportation.

This may seem a little disgusting - yesterday's feces, urine, breath, skin flakes, clothes, etc, are all spun into today's consumption. But it's been what we've each been doing since before we were born. We're already part of the water cycle, carbon cycle, nitrogen cycle, and many other cycles of biology. If you're eating a strawberry today, some portion of it was manure a month ago.

The Decomposer/Feed/Compiler system merely speeds it up, minimizes movement of dumb atoms, and applies the idea of perfectly recreating the template that you want. If they figure out how to perfectly recreate the Best Strawberry, then you get that one whenever you want, without blemish, insect, or age since it was harvested. Better yet, given that scanning an object for a template takes time, and templates can be manually reviewed to take out imperfections, you can having a really perfect strawberry, something that could never be enjoyed in a real city.

Each city now resembles a flower taking in power from the Sun and other sources, and endlessly recycling and rejuvenating itself.

The numbers don't add up, with current technology, for a sustainable system.

Plants are the most efficient way to convert renewable energy into food, but "the most efficient" doesn't mean "efficient". The maximum power input from solar energy is around 1kW/m^2. Plants convert that energy into food with an efficiency of at best about 3%, and that assumes the entire plant is edible. That means plants are converting a maximum of 30W/m^2 - when the sun is shining and there are no clouds. Averaged over a year, the day length is 12 hours out of 24 which reduces the average "edible energy" to 15W/m^2. Factor in the influence of weather, and any other inefficiencies, and you might get a number like 5W/m^2 averaged over a year.

A sedentary human needs around 100W of power for survival, and more to actually "do stuff." So one human needs at least 20 square meters of "plant growing space" to stay alive. And if you try to feed yourself entirely from a 5-meter-square vegetable patch, you will soon discover that is a rather optimistic estimate!

The population density for New York City as a whole is one human per 100 square meters, though in the densest areas (e.g. Manhattan) that is reduced to one human per 30 square meters.

So the bottom line is that literally every available space in the entire city would have to be devoted to high-intensity farming, for self-sufficiency. No space available for basic infrastructure like roads - every available space would be needed for food production.