I've always enjoyed coffee shops (as they all have free wi-fi now, even in small towns!), but you do have to briefly interact with the barista to order coffee or tea. I think it helps if you have an idea what you want before going in and/or always get the same thing.

Library is a good idea if you don't want any interaction at all, though.

Or if the weather's nice, and you have a park nearby, maybe take a book there or something.