First off, Tavern on Green, which is on Green Street in Philly's art museum area, is named as a joking nod to Tavern on the Green. Don't get scared that you'll be spending your kid's college fund here. The prices are cool.
This place had Celis White two weeks ago. That alone is worth a trip. I haven't seen Celis White in a Philly bar or liquor store in many, many years. There are many other bottles available, with a lot of local favorites (Victory and Flying Fish, for instance), as well as some West Coast beers and well-chosen imports. I was happy to see two types of Weihenstephaner available.
The place tends to be quiet, and is therefore really good for conversation. There's outdoor seating along a nice, moderately traveled neighborhood street, a slightly upscale seating area, and a regular joe bar area. Whatever you're in the mood for, this place can accomodate it...unless you're in the mood for upbeat, hip, and lively, because Tavern on Green isn't that. It doesn't get a big, energetic crowd, as far as I can see from my visits. Maybe there is a time when the crowds rush in, but don't count on it.
I recommend this place as a nice change of pace, particularly when you want to shift into a lower gear and mellow out.