What does it mean when you ask a guy out and he says no but keeps smiling at you?

It could mean he's pleasant and friendly - but simply chooses not to go out with you. That's OK - he sounds like a good guy.

Or, it could mean he does want to go out with you - but he wants to be "begged" a little more. That means he's a self-centered creep, and you're better off without him.