Obviously, keep your eyes on the gauges, but I think the likelihood of much running in Utah during your timeframe is actually pretty slim. Rivers here typically don't run until mid-late May. While a few things can often start up in mid to late April (Riverdale, Oggie Canyon, Scrambled Egg Bend, etc.), that is sporadic from year to year and I wouldn't count on it this year given the crappy snowpack we have (in No Utah). I'll be (happy, but) shocked if Oggie canyon and Riverdale come up to decent flows at all this spring. That's how bad the pack is. The black boxes of the San Raf are quality (self-support, decent rapids and incredible scenery), but again, usually a later timeframe. I ran it at the very beginning of June in 2006 the last time we had a massive Southern snowpack (which we have again this year). I can't see the upper provo running in April either, and access is probably going to be an issue as the road is not maintained during the winter. You may have luck in So Utah, NF Virgin, Timpoweap canyon, etc. Those are unreliable in normal years so I can't remember when they typically go.
For April, there will of course be the standard runs around Hood (Farmlands, Truss, probably Wind, Little White, etc.). Maybe the Payettes, just north of Boise (not sure if that's too early there or not), Lochsa and other panhandle rivers and creeks (seems early for those too, but others on the thread seem confident the timing is good). Black canyon of the Bear (Grace, ID) on 4/18 - scheduled release.
Hope you find some good boating options, just didn't want you to bank too much on Utah having water.