Hi and welcome Mari! Thermopolis is a really neat place to visit. You should definitely make your way to one of the hot springs pools/hot tubs. The Tipi one is more quiet, less kids

Star Plunge is nice too but it is a hot spot for the younger crowd.
You have to visit the Four Winds Trading Post! You'll find some like-minded friends who own the store. I have not eaten there except at the Holiday Inn & Safari Club and it is pretty good, no complaints. Great place to visit to see some interesting animals (taxidermy) and really cool pics of safari trips. Prices are average. There is an Italian restaurant that was recommended to us but we have yet to try it out.
There are several stores to browse through, bookstore, boutique type store, etc. There is also a dinosaur musuem if you're into that. I think it costs about $15 to tour - please, someone correct me if I'm wrong on the price. It's kind of a small museum but they sometimes have bus tours to another place to see where the dinosaur bones were found/are being found.
Anyway, stop by the Four Winds store and the folks there will be better able to recommend or not recommend places to go. HTH.
Have a wonderful and safe trip!