Whether you've got your own corner of a rooftop terrace, a shady Brooklyn backyard, or just a reasonably sunny window sill, every New York apartment can accommodate at least some kind of gardening. The trick is knowing what kind of plants will work in what kind of space.
DNAinfo has a beginner's guide to apartment planting, and as you'd likely guess, what kind of plants will grow in your home is determined almost entirely by the amount of natural light you get (if you're working with an honest-to-god outdoor space, you can try just about anything, including "flowering" plants that don't tend to grow indoors). That, and watering; according to experts, you should actually check for drying in the leaves as a sign to water, rather than looking at a plant's soil.
If your room is bright enough that you could, say, read a book without turning on the lights, you can start off with basic, hearty herbs like basil, parsley, oregano, thyme, sage, and maybe even cilantro and dill (these can work in a window box or just on a well-lit sill). If you're working with a little less sun, the site recommends snake plants, ZZ plants, rhododendrons, or Chinese evergreens.
Failing that, you can bring in the gadgets—like plant lights, "vertical indoor gardens," or options like the AeroGarden or Click and Grow—and if you're still on the fence, the site has a quiz to help determine which plants are right for you and your apartment (we got "tomatoes, herbs, and peppers," for what it's worth). No time like the present to cultivate a private stash of basil.