Hot Springs: Lava Hot Springs in Idaho, never been there, but I believe they have water slides and stuff.
If you are in SLC, go to Burger Bar in Roy, Utah. Old style burger joint with great shakes and burgers, including burger made from game meat. It was featured on Diner, Drive-ins and Dives.
Milt's Stop and Eat is a super old fashioned burger diner in Moab.
Look online for indian ruins. We found some neat ones west of Blanding.
There are some fantastic movie theaters in SLC and the summer movie releases should be out.
I have always wanted to fish for trophy Kokanee in Flaming Gorge. Your timing would be about right I would think. That is when Kokanee get going here in Oregon.
Cabela's (SLC, Grand Junction)
Scheel's sporting goods in SLC (crazy big)
If you are willing to detour south, the striped bass fishing in Lake Powell should be off the charts in June, out of Page AZ or Bullfrog UT. That detour can include hiking in Bryce Canyon. The natural canyons in Bryce are unlike anything you've ever seen.