Looking for destinations

How much of a four-wheel drive challenge are you looking for?
 
What time frame more specifically?

Probably around late June - early August

Those are good months for the Colorado Rockies. The famous trails around the San Juan mountains would be near the top of my list.

The Canyonlands of Utah would also be near the top, but just be mindful those will be the hot months.

You can also stay on the dirt between those areas on trails like the Rimrocker if you have plenty of time.
 
Moab, UT (iconic red rocks, hikes, mountain biking) or Colorado Rocky Mountains (Pikes Peak, Rocky Mountain Nat'l Park) Long drives but iconic landscapes. Give yourself 2+ weeks.
 
If you can't get out west. Maybe North? North Maine Woods, Canada and their Maritime Provinces