I end up in the Gallery Place-Chinatown neighborhood about monthly for dinner, but almost never for Asian food. Recently went to Daikaya, which was rather interesting and OK -- very loosely Japanese! There is a Japanese-themed place very close to the Ren that was OK; can't remember the name. I do like Chinatown Express for cheapo, non-fancy experience.
Non-Asian I like include Graffiato, Zaytinya, Proof, Jaleo, Rasika (ok this is Asian -- Indian), Arcadiana, Corduroy (more expensive).