Brother Bear,
Living here in Northern Utah, I could give you some suggestions of a few. There's not that many that I'm aware of.
Right now I'm in Lompoc, CA on business (stuff and Vandenberg AF and will probably be visiting Gaviota (sp?) Hot Springs this afternoon after work.
But two good ones in Utah are:
Ogden Canyon Hot Springs. (Just next to the Ogden River at the mouth of Ogden Canyon) They are nearly right under the large Pipe that suspends 100 feet or so across the mouth of the Canyon.
By far the best is Diamond Fork Hot Springs. It is just past the Diamond Fork Campground. The turn off is about 9 miles up Spanish Fork Canyon (from the Springville area).
Send me an e-mail (Wizard has the address) and when I get back in town, I'll be able to send you some directions and some pictures if you like.
I think there are a few other obscure Utah Hot Springs, but I haven't been to any others in the state. Now if you're talking about IDAHO... theres' some awesome stuff about 5 hours north of Salt Lake. That state is a Hot Pottin' Heaven!