A few ideas:
The Roosevelt -- beer, wine-by-the-glass, interesting takes on classic bar snacks; the only downside is that it's half a mile north of the arena, so be prepared for a good walk. Get off the train at Roosevelt / Central if taking light rail.
District -- ground floor of new Sheraton; good food and beer selection; wine selection just okay; short walk to arena via 3rd St through Convention Center
Kincaid's -- steak and seafood place, but has a nice bar in which food is also served. Very close to arena
816 N 3rd St, Phoenix, AZ 85004
Kincaid's Fish Chop/Steakhouse
2 South Third Street, Phoenix, AZ 85004
340 N 3rd Street, Phoenix, AZ