You can definitely start with your local LBS. Most shops are pretty cool in telling you how to do minor stuff yourself besides the basic tools" you would need.
I think this forum has a thread that lists bike cooperatives, kitchens where they would show you how to take care of your bike. You can also google "bike cooperatives, kitchens, instruction, NYC" and see what that brings you.
I wouldn't be surprised if there is one you can go to. Hell, you live in NY. I'm sure there is one you can go too.
Count yourself lucky that you don't live in the boondocks, like me, where it is mainly DIY.