Maybe go to Mesa Verde, CO, passing by Aztec Ruins and Chaco Culture NMs? Then on through Hovenweep, Valley of the Gods and Natural Bridges NM? Take a peek at my SW trip report filed 2 weeks ago.
River was down enough in Zion a month ago that there were lots of people up the Narrows but still rent a staff and drainable boots.
You could kill 1/2 a day at Cedar Breaks (which overlooks Cedar City). Best viewing seems to be just before sunset so you can drive from there to Cedar City (or stay at Brian Head).
It should be quite cool at the high elevations (or warm-ish during the day, and cools down a lot at night).