We were there last year. We stayed at the Grand Canyon railroad camp ground in Williams, az. Very nice place. We made the reservations for the campground, we also made them for a round trip on the train to the south rim and a hotel for an overnight stay. There is a lot of walking so staying overnight was great. The kids will love the train ride.
We took a pink Jeep tour in Sedona, az out on the red rocks.
In New Mexico near Las Cruces is White Sands National Monument. Kids can sled down the sand dunes.
San Antonio has the river walk and the Alamo
Houston Johnson Space Center
Bill