Look at Days Inn or Super 8 hotels in Rapid City. They're all pretty cheap ($35+ per night) and they're all really clean. I like Days Inn because they have continental breakfasts!

Avoid motels along North Street. They're all roach dives with neon signs and they have monthly rates.
A really popular restaurant for tourists is The Firehouse; it's in an old fire station downtown. Other local restaurants are Delmonico, Botticelli's, Enigma, Wine Cellar, The Corn Exchange, and Tally's. They're all within a few blocks of each other downtown too. Oh, and check out Prairie Edge gallery! I can't think of much that is really going on in December. There is a charter bus that takes people around the city to look at Christmas lights. Too bad you missed the Parade of Lights, it was last week. Hmm... Most of the stuff you'd want to see is up in the Black Hills. I don't know if you've seen Mount Rushmore or Crazy Horse before but those are the two most popular destinations and it takes about 20 minutes to get to them from Rapid City.
You said in a previous post that you went to CSU. Rapid City is a lot like Fort Collins. They're about the same size and they both have a neat downtown scene.