The creeks and rivers are low volume... better suited for kayaking. I've boated several sections on both the Logan and Weber rivers (glad to be in a kayak, I would not raft them). It is a four hour drive to get to good rafting. It is a four hour drive up to West Table to Sheep Gulch. Alpine canyon (Snake river) is ton of fun. Pool and drop class III. Take a surfboard for Lunchcounter.
Westwater on the colorado is too high for someone unfamiliar with the lines (also a four hour drive).
Four hour drive to Gates of Ladore and similar drive to other epic multiday trips. But these require permits.
You should run Alpine canyon. The water is cold. It comes out of the bottom of grassy lake reservoir. Do your kids have wetsuits?