Really the only day boating is on the Colorado River above Moab (Moab Daily). The road is right next to the river for 5-6 miles above Moab and this stretch is pretty much Class I.
Above that stretch is the Castle Valley and the river is mostly away from the road. This stretch is Class III- ish and is the stretch you want to run. There is an obvious put in at Hittle Bottom at the upstream end of Castle Valley. Putting in here requires about 2 miles of flat before the rapids start. There is another put-in just about the first rapid (Little Professor), but I don't know how to describe it - just a nondescript unmarked little dirt road. The full run down the valley is probably 6 miles or so. The best takeout is about 1 mile downriver of Castle valley (into the mellow stretch by the road) and is called Sandy Beach. There is another obvious takeout below Sandy Beach, but it is packed with commercial take-outs during the summer.
Upriver from all this is Westwater Canyon, which is Class III-IV, but requires a permit.