Hackerspaces generally have machine shops, but that's not all they are. They also have lounges, computer labs, biotech labs, kitchens, and whatever else their respective members are interested in.
I find it doubtful they'd charge you just to check the place out.
Definitely not! The place is open to visitors most every evening. Any of the events on the calendar are open-house events: http://atxhackerspace.org/wiki/Calendar
Diplomacy is the art of saying "nice doggy" until you can find a rock.