We're headed to the Grand Canyon again this spring and beyond for a couple of months. Places we'll stop on the way to the Grand Canyon include New Orleans (WW II Museum), Galveston (beach camping), San Antonio, Carlsbad Caverns, Alamagordo, Saguaro NP, Sedona.
Besides the Grand Canyon, you could easily spend weeks in the Four Corners area at the great NPs mentioned, and so many state parks too, like Goblin Valley in Utah with its interesting rock formations. Kids would enjoy that, along climbing the ladders at the ruins in Mesa Verde.
Moab is a great base for the Arches area, and there are lots of campgrounds there and nearby. Plenty of kid-friendly hiking opportunities. Don't miss Island in the Sky section of Canyonlands NP and the Dead Horse Point State Park.