The stretch from Cisco landing to Dewey Bridge is pretty flat and there is a lot of ranchland that is privately owned. From Dewey Bridge down to Moab would make a nice overnighter with a little more action. Although you have the highway on river left, there are some nice campsites on river right. There is one really nice beach in the vicinity of Professor Creek. No charge and legal to camp on river right if you are floating down.
Pagosa to Navajo: With enough water ~1500 or so, this would be a nice Class II - III- trip. You can spend a couple nights on the way to the reservoir. I have heard there is an easy takeout where the San Juan comes into Navajo.
Gateway to Dewey Bridge: With enough water in the San Miguel, this would be a nice float on the Dolores.
Escalante to Whitewater: Nice little float trip. Camping and sidehikes at Dominquez canyon is excellent. Could be very crowded on holiday weekends. Can be done as a day trip with a takeout at on Bridgeport Road (kind of a swampy takeout with mosquitos).
Piedra down to Navajo: With enough water? Has anyone done it?
White Rock Canyon: On the Rio Grande. Has anyone done it?
Ute Mountain Run: On the Rio Grande. ???
Also, there are a few overnighters on the Upper Colorado in the Pumphouse, Burns area.
How old are your kids? Mine are 3 and 5 and they love to do trips like these. I am sure I have seen you around, but haven't met you yet.