Last fall, when I went to Missoula I stayed at the DoubleTree and at Ruby's Inn.
The DoubleTree was nicely located close to downtown and from Mount Sentinel, so it was a great place to stay for exploring the city. Their restaurant has a really nice view on the Clark Fork river. They have a free shuttle to and from the airport.
Ruby's is not as fancy and not really walking distance from downtown, but it is very affordable. They also offer a free airport shuttle.
For those considering camping and traveling by airplane, there is a REI in Missoula where you can rent camping gear. That is a good option too.
I love the Come On Inn in Missoula. Todd and I used to do a StayCation on New Years and rent a Jacuzzi room, back when I was less caring about the impact of endless private baths of hot steamy water and a big screen TV.