Below the Westwater takeout (Cisco landing) to Dewey Bridge or further is a beautiful stretch, just avoid camping at Fish Ford as there's road, and thus redneck, access there. The Green River from the town of Green River, UT to Mineral bottom is another good 4-5 day float (at high water, 3 days if you put in at Ruby Ranch) but just make sure no one will be terrified on the really hairy drive out of Mineral bottom.
PS - there's no road from the confluence of the Green and Colorado, just a really expensive jet boat to bring you back to Moab.
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse