I took out at Fish Ford one time, which is about another 4-5 miles down from Cisco. The camping at Fish Ford is nice because there's a ton of big cottonwoods next to the river, plus an outhouse (last time I was there, anyway). The downside is that you might not be alone because it's road accessible. Regardless, there's a lot more tree shade throughout that stretch, and I'm sure there are more private options on river left.
It is a scenic laid back float. No rapids to even speak of. You would be hard pressed to find even a little whitewater. The first few miles is very desolate, but as stated above, once you get to Fish Ford it becomes roadside. Before it becomes roadside there is plenty of great camping spots but the underbrush is thick along the banks, so finding a good place to dock for the evening could be tough. If you aren't looking for any action it is a great trip!
I put in at Cisco last year...camped at Dewey and ran "Moab Daily" the next day. Great views of the La Sals. Fun trip; it was running 27,000 !!!
I would camp before Dewey being it crowded, especially on the Fourth, let alone any day in Moab.