Old Chicago Pizza in the Central Texas Market has great local beer on draft and tap and plenty of screens (pizza not too bad either).
Crickets downtown has more beers than you can shake a stick at and plenty of screens (burgers and cheese fries).
Lots of screens, their own beer and a huge menu at BJ's Brewhouse at the Richland Mall.
A sponsor here is Barnett's Pub downtown, which is a great place. Pub food, very large selection of whiskey and whisky, good beer selection. Never been there to watch a game.
Coach's Smoke BBQ downtown. Never been there to watch a game. Ok BBQ, beer selection is pedestrian, but that's a matter of taste.
For upscale, sit at the bar at 135 Prime on Hewitt Drive. Nice steaks, nice wine list, upscale cocktails, big screen right in front of you. Same thing would probably work for Diamondbacks down town. Its next to Crickets.
If you are staying at the Indigo downtown, the restaurant/bar is good there (upscale cocktails, nice beer selection. The wine is expensive if you get anything that isn't mediocre.)
Illigitimus non carborundum