In the summer here (June-early Sept) we grow what we can, i.e. that has a short enough growing season. Usually we do lettuce, swiss chard, broccoli, cauliflower, beets, carrots, spinach, zucchini, green beans and a few cabbages. We also have a greenhouse where we grow tomatos and cucumbers. For fruits we grow rhubarb, raspberries, currents and strawberries. We also buy local when we can. The season for farmer's markets is also short (they don't get any special weather yet). The rest of the year I get fresh veggies from a CSA in Washington state. It's about as "local" as I can find fresh stuff. At least it doesn't come from South America!
Schmoodle - I get a list on Thursday for what will be in my CSA box on Tues. It's enough time that I can arrange my other shopping to accommodate what I'm getting and I can substitute a certain number of things if I don't like them. I have fun looking for recipes for things we don't usually eat.
I've kept chickens in the past, and they are entertaining as well as giving you fresh eggs.
Again the winter is what makes it difficult. I kept them through the winter several times, but they stop laying and require a lot more care - which means higher electric bills and no eggs to offset that cost.