How to help people in my neighborhood who won't ask for it?

I live in NYC, and since last year have noticed more and more people in my neighborhood who can't pay for groceries at the checkout, and who are talking about losing their jobs because they can't afford childcare. I was in line behind a man today with his young son, and he was buying cheese and a loaf of bread for 2.50, and didn't have enough in his debit account to pay for them. After he left the store, I paid for them from the cashier, and tried to give them to him discreetly on the street, but he said he "couldn't take welfare and couldn't take handouts". It killed me, because my parents were the same way, and though they taught us self reliance, we went hungry a lot. I'm a student at a public university now, and only make enough money with my part time job to pay for rent and food for myself, but I know there's people in my neighborhood who are too proud to ask for help with the basics, even when they have kids, and however tight my finances are, I know I could do something. There are a gazillion programs in NYC for kids, but the programs can't get to the kids if parents don't want to use them. Is there anything I could do that's less of a "hand out" and more win-win? I've thought about posting a "teach me how to cook" thing on Craigslist (I'll do screening and all that before letting anyone into my apartment), where I pay for the materials/groceries, and we split the food, or doing free tutoring for kids, and having lunch or dinner for them. I'm very sensitive to people who don't want to feel like their getting something for nothing, so I want to be able to have a more equal relationship. Any ideas?