Ya the watersheds are not that big in UT; and the creeks near some of the best skiing (LCC/BCC) are too steep and woody for paddling for the most part. American Fork (watershed south of Alta/Snowbird) is slightly more kayakable, but its steep, low volume creeking with tons of wood.
The Provo, Weber and Ogden can be good, but are dam controlled so it takes a big year for the class 4 runs (Provo: Bridalveil, Weber: Eggs, Ogden: Narrows) to come in. I saw some folks run a shredder down the Ogden Narrows once. I don't recall seeing a full size cat on any of these.
The upper Logan is a very nice undammed 4-; but very narrow, brushy, never seen a cat on it. Roadside scout for the Monolith crux. You know how spring is, everything runs at once; so you often have to choose between Logan, upper Provo, Price, Ogden Narrows (and all of Idaho, WY, etc)..then its all done.
The Webers class 2/3- Henefer to Taggart, that is the most reliable summer water around here; its just getting shut off right now. Its between an interstate and a railroad, with ridiculous numbers of tubers on summer weekends. I don't remember seeing a cat on it; there are commercial rafts tho. There is a low bridge in Croyden, much discussion if oar rigs fit under it. Weber State will not rent their small rafts for the Weber in the summer; they say they get too beat up (?). Seems to me a little Puma would be perfect. Or an Aire inflatable couch
The Snake's Alpine Canyon, and Greys, are 4 hours away, Payette area is about 6. Its so worth it to go up there... even last weekend, there are still some cat boaters running the lower 5 every day. Even the "warmup" still has big sections (at 1080cfs!) (as well as some rocky sections).
If you like big water you would love the Lochsa in the spring...
Black Canyon of the Bear only runs for 4 scheduled release weekends in early spring; its cold; and often a powder day with the lifts running.
Murtaugh I am not too familiar with; various levels seem to run at random times, dam released; it can be huge in a big spring.
For easier big runs there is the Green River daily, and Moab Daily...
Westwater on the Colorado needs a permit, runs all the time; that is right on your way from Golden to SLC.