A range of nearby options:
Ping Pong Dim Sum--not traditional cart-rolling dim sum, more like modern Asian in a hip, lounge environment
Corduroy--American fine dining, but on the casualish side, not uptight
Acadiana--Louisiana cuisine in an upscale environment
Del Campo--South American style meats
Busboys & Poets -- Southern food in a young hip atmosphere
A couple of blocks further west, there's Bibiana (Italian fine dining and cocktails) and Capital City Brew Pub (self-explanatory). A couple of blocks further south, there's Gallery Place/Chinatown, with 1,001 options.
I would avoid:
Kushi (you don't like sushi, and the non-sushi isn't that good)
RFD (many beers, but concrete floors and frat boys in ball caps)
Cuba Libre (everyone who's been says it's horrible)