How to evaluate a used bike

[PamNY]

I really need a beater bike that I can lock up without worry. So I'm looking at used bikes.

I can judge the obvious -- if the brakes work, if it shifts, etc., and I can get help with DIY if a bike needs basic tune-up work. I expect to spend some money and time on a used bike.

What I'm worried about is the frame and wheels. Will problems be obvious to my naive eye? Do I need to remove the tire to evaluate the wheel?

I'd appreciate any advice. I don't care about cosmetics -- in fact, for locking up in NYC, the worse it looks, the better.