You also got the Ogden Wave. I assume you mean kayaking and not rafting right?
If you don't mind driving some, you got the stuff down south: Green River daily, Moab Daily, Westwater (class 3).
Local would be the Weber river in Ogden. Henefer to Taggart would be up your alley Weber River - Henefer to Taggert - River Brain
Up north there is Snake in Wyoming (3.5 hour drive), also Murtaugh canyon on the Snake, but it's class 4.
As Toshkya said, Provo river is an easy class 1-2 float. Very pretty and easy to shuttle.