I really enjoyed the article Marie mentioned in the post below, "The Art of Self-Reliance." I didn't realize that there was a whole movement of backyard bloggers, but I suppose the more coverage of it there is, and the easier people view it, the more likely it is that people will realize that they too can do it.
Start small, and grow a couple of tomatoes and peppers in pots on your patio. That's what I did. I used to have a small apartment in Virginia, with an even smaller third floor balcony, not much bigger than a case of Bud. But I was able to grow vegetables in planters and hanging baskets quite easily. And I've been "cheesemaking" for years.
As far as a new name, I'm not sure what a better name would be. I have to admit that I, too, feel that calling what we are doing backyard "farming" is a stretch. And I have always slightly bristled at the term "homesteading." It makes me think of the Trail of Tears and blankets infested with smallpox.
I definitely like the word urban as part of it. "City" would be good, but I feel that that would leave out the suburbs, which sometimes can feel like they lie outside of the space that makes up the city environment.
So--no "farm," no "homestead." "Victory Garden" seems dated (especially since no "victory" seems to be in sight), and "greenspace" feels more like a city parks and recreation term.
I like the word "patch." It definitely alludes to gardening, beds, or a small tract of land. Urban patch is not at all catchy, and even sounds like some kind of city renewal endeavor--or worse...
What about Green Patch? Start your own green patch. You mention at a cocktail party, "I have a green patch." No, that might draw funny looks from your audience. Especially if you say that you your neighbor sometimes complains of the "fowl smells coming from your patch." Hmmm, a bit too English sounding maybe.
I challenge others to continue this chain of thought.
This may or may not require the ingestion of alcohol or mood altering drugs.