Blackbird, Avec, and The Girl and the Goat are all good choices aht the ones that came to my mind first give the criteria you outlined. Fairly inventive food, casual atmosphere. "Fun" youngish foodie crowds.
Topolobampo or Frontera Grill if you like Rick Bayless' food. it's Mexican influenced, not Tex-Mex. Most people either love it or can take it or leave it.
I'm very fond of Custom House. More low key, but very good food and a reasonably priced wine list. I love this place and think it doesn't get enough credit. One is not out of place in either a coat and tie nor in blue jeans and a starched shirt. My kind of joint.
http://www.customhouse.cc/
Les Nomades or Alinea if you're into the big restaurant, big meal deal. Les Nomades is the old line, formal French restaurant. I'm very fond of Alinea. It's more nouvelle American.
http://www.alinearestaurant.com/
Naha is somewhat in the same category as Alinea.
Tru is the most cutting edge French influenced French restaurant in the city. Quite good. Excellent wine list, but high on the markups.
I know it's not what you said you wanted, but Charlie Trotter's is an interesting place to eat if you're really into food. Preparations are inventive to the point of being almost too precious. Quite interesting. Very quite and subdued atmosphere, however. Impeccable service. Everybody should eat there at least once.
