We dined at the renowned Cafe Pasqual's, which serves good Southwestern style cuisine in convivial surroundings. There is a communal table where people seem to meet and talk to strangers and generally have a good time. This place is mobbed at breakfast, but I can't say anything from personal experience.
Another good place was Ristra, also for Southwestern food, where we discovered elk, which is a tasty, healthy alternative to beef, which my wife can't eat.
For Southwestern food, a better bet is Coyote Cafe, where it was more or less invented 30 years ago. Here the food was interesting and very well executed.
Shrimp tower and roast and confited chicken at the Coyote Cafe
One night we had a late meal at Shibumi, a new Japanese noodle place, where the ramen and izakaya (pub-style) dishes were quite authentic. This is a new venture of the chef owner of Nostrani, a highly rated Italian restaurant that we didn't get to. He trained for a couple of years at the New York branch of Omen, the famous Kyoto noodle restaurant, so the authenticity is well-earned.
But my personal favorite was Bobcat Bite, which is worth its own post.