This is my neck of the woods. Let me know if you want beta on anything. Grand Mesa, Dolores Canyon, Uncompahgre, Weminuche, La Platas, San Juans, Lone Mesa, Hovenweep, Canyon of the Ancients, etc.
Would not recommend going to Moab in July unless you're planning to run the Green. Best times are April-May, or September-November.
@asava, we are planning to camp near Durango for approx one week. One day for narrow gauge railroad, at least one day for Mesa Verde, maybe one day for Ouray hot springs/Oak Creek Overlook, one day to hike a bit on Colorado Trail. Do you think kids would like Canyons of the Ancients?
Will take recommendations from you and tdaver to defer Utah rock formation national parks to a spring/fall timeframe.
DGO in July is great, though you should be aware that the rains/monsoons usually start about mid july and set in just after noon. The snows should be melted up high, and there are lots of amazing day hikes you can get in while around, and several I'd recommend over the Colorado Trail section that is down here. Check out Engineer Mountain via Pass Trail at the top of Coal Bank and take it to the meadow. Summiting Engineer is a little bit of a scramble, so it would depend on how old/adept your kids are if you wanted to try and get close to 13,000 ft. Either way the meadow is awesome and the views are incredible. Just don't get caught up there after noon, as you'll be above tree line where clouds move in quickly and lightning is a deadly concern. There are also lots of hikes off Molas Pass as well. Check out Vestal Basin. Lots of waterfalls and it's hiking only, but that will take you on a portion of the CT that is only open to foot traffic. Molas and Little Molas have great campgrounds as well. You could also look towards high alpine lakes like Highland Mary Lake, Columbine Lake, or even Ice Lakes. Ice Lakes is permit only now due to so many people finding out about it via instagram and it basically being overrun by idiots who start fires and generally leave crap everywhere, but it's a pretty remarkable place. Highland Mary and Columbine are lesser known and good options. An easier lake hike would be Potato Lake near Purgatory.
Canyon of the Ancients is awesome, but your kids might lose interest if they've already done Mesa Verde. Depending on where you are camping, it could mean a lot of time in the car. You're doing the right thing by giving a full day or more to Mesa Verde. It takes quite a bit of car time just to get to the dwellings. You should also double check to see what sites are open. They often close sites for restoration, and it can be a big bummer if you go in there without knowing some of the more accessible ones are closed.
It sounds like camping at Molas or Little Molas would be your ideal location to reach both Ouray, Mesa Verde, and do a bit of hiking. Andrews Lake, Molas Lake, and Little Molas are all great to do a little stand up paddle boarding on. Where were you thinking of camping?
Personally, I'd try and not do too much. There's plenty to do and not enough time around these parts. I've spent the last decade exploring all that I can and still have so much on my checklist to knock off. Pro tip on the narrow gauge: one way is enough. A full day on that thing feels pretty long. Purgatory has a lot to do and they've built out a ton of stuff recently, new alpine coaster, a lot of mountain biking, etc...