I've been to Speakeasy 3 or 4 times, and highly recommend it. I know it's been mentioned in other posts - you might try searching for it. Jody also runs South, on Broadway, anoher excellent BYOB. Frankie J's, which combines improv with good food, is fun, but I vaguely recall hearing he got his liquor license recently.
Of course, if you want to go ethnic, there are tons of options.