I've been there at least 15 times, motorycle, snowmobile and car. The worst place you can stay is the Super 8 in West Yellowstone. It's 10 miles west of town all by itself with a little resturant next door. Nothing to do, nothing to see there.....
Having said that, West Yellowstone is the only town close to an entrance to the park. It has many hotels, both chain and independent. I've stayed at the Stage Coach, Holiday Inn and others. A quick search show a BW right in town for $71/nite.....I'd suggest a google search and:
http://www.trails.com/all-hotels/city-hotel.aspx?dest=MT+West+Yellowstone
I wouldn't stay in Cody, Jackson Hole or Livingston, all a ways from the park, book solid and expensive also..........