We were in this area just a few weeks ago. Here are some of the places we stayed.
Duck Creek RV Park in Las Vegas. If you like mustangs make reservation to visit the Shelby Museum while in Vegas.
Watchman CG in ZionBryce Canyon/ Ruby's Inn We didn't camp here we just drove up for the day from Zion.
Hitch-n-post RV ParkIn Kanab, Utah. Tight but it is a convenient place to stay to visit the North Rim of the Grand Canyon (which is even more beautiful than the South Rim (just my opinion).
Page, Arizona Lake Powell Area See
Vermillion Cliffs,
Horseshoe Bend. Go walk out on the Dam Bridge and drive around Lake Powell. Lots of interesting stuff here in Page.
I've not been to Mesa Verde but want to go but you need to go over to Durango and stay and ride the
Durango/Silverton Train to visit the old west town of Silverton. You can rent jeeps here to take the
Million Dollar Highway and the many jeep trails up into the mountains. You could stay in this area for a week or two and never lack for something to do.
The State Parks in New Mexico are awesome also. We just spent a whole month there in them all over the state.
Anyway, have fun and enjoy those kiddos! Make some memories!