FnB has the best selection of AZ wines (along with super knowledgeable staff) and their food is very good farm to table.
Atlas Bistro has excellent food and it's one of the few fine dining BYOs in town
Chula Seafood has incredibly fresh seafood (both served at the shop, mostly as bowls and a fish market for take away) in a casual environment.
Kaziemierz Wine Bar has the biggest wine book in the state and some of the listed wines are actually in stock.
Little Miss BBQ is true Texas / Austin barbeque. Get there before 10:15 for the 11am opening. No frills. Fatty brisket is king.
Kai is native American influenced. Superb food and service. Excellent wine list. It's the only 5 star/ 5 diamond restaurant in the state and our favorite splurge place.
The Gladly has very good food, especially on days that their raw bar is open.
Rosita's Place (on 24th and McDowell) if you want Sonoran style Mexican.
Tacos Chiwas for Chihuahua tacos.
If you want cocktails at all, that's an entirely different discussion.