Suggest that you head south first before the weather gets hot. Visit Zion than east to Lake Powell.
From there move over to San Juan county and visit Monument Valley on the way. In San Juan County, stay at the Cadillac RV Park in Bluff and visit Hovenweep Natl Monument, Valley of the Gods, Natural Bridges Natl Monument.
Then move over to Cortez, CO and visit Mesa Verde.
From Cortez, move to Moab and visit Canyonlands and Arches. Plan on staying at least a week there.
From Moab, move to Torrey to visit Capital Reef. From there go to Bryce before heading back north.