BrianB,
Hill AFB has a very nice skeet and trap range, they also have a fun 5 stand course set up. A round of skeet/trap is relatively cheap (last time I was there it was $3.50) and 5 stand is something like $5. The suggestions for the Browning Museum are good ones, its a neat place with alot of interesting stuff. This has nothing to do with hunting or guns, but if you want to see/go someplace really nice, take the short drive north up to Bear Lake. Its beautiful and theres a small shop there that has the best milkshakes ever made. You could also grab a fly rod and fish the Weber river around Devils Spine turnout, lots of browns and you'll have good luck on the whitefish as well. Lots of fun things to do in Utah, and the women are nice to look at too.
Dustin