Like Alex said, there really is not any good place to park. I usually just opt to valet whenever I go down there - it's usually reasonably priced and that way I don't have to circle the Short North for an hour trying to find a spot. I'll pay for the convenience.
Also, just wondering, did you guys know that Union is one of the largest (if not the largest?) gay/lesbian cars in the city? I've had friends from out of town want to go there...until I tell them that the chicks there likely won't be into them. Of course, I'm being a little stereotypical, as plenty of straight people go there, too. But, still, just wondering if you guys knew that.