Lived in Missoula last year:
Tamarack is a great combination of beer and food. The chef and Brewmaster coordinate to match what is brewed with what is cooking. Fish & Chips and the French Dip are both the best I have had anywhere.
Top Hat is a great place to have lunch and has great music at night. It is part of the same group that owns The Wilma Theater and Kettlehouse Amphitheater.
Hob Knob has really good breakfasts.
Not in a fancy setting (strip mall by Albertsons and Office Depot) but Ambrosia has excellent Greek Food, It is on Reserve Street. The Greek Fries are a must order.
Things to do:
Walk along the Clark Fork at Caras Park and watch the surfers riding the whitewater area.
Drive up to the Snobowl Ski Area for spectacular views.
Make a drive down to Phillipsburg aka "P-Burg" funky old mining town with a brewery, some good restaurants, Sapphire mines and the biggest, best candy store you ever imagined. Be sure and drive up to Georgetown Lake if you go there.
The National Bison Range is about an hour north of town, Beautiful scenery and a chance to see every animal you would see in Yellowstone without a traffic jam, or maybe anyone else in sight.