Camping road trip

Forgot to mention, this will be in Summer or Fall sometime... So colder areas are fine.

Try the North Shore of Lake Superior, in Minnesota -- there are a ton of beautiful state parks. Some of them are walk-in sites, some are "cart-in" (you load all your stuff into a large wheelbarrow-type thing), and others are typical drive-in car sites. Here is a clickable map listing all the state parks in Minnesota -- click on the ones on the North Shore for more details. One of my favorites is Split Rock, with beautiful cart-in sites.

Fall can be a great time to visit the canyons of southern Utah. There is excellent camping in all the national parks there and if you really want solitude and don't require any amenities you can camp almost anywhere that strikes your fancy off of the many miles of BLM and Forest Service roads. I would especially recommend the Escalante area and the Butler Wash north of Bluff, UT. The northern part of Capitol Reef (Cathedral)is accessed by a good gravel road and is beautiful as is the scalloped ridge to the south of the highway (Cedar Mesa). Further north, there is good camping in the San Rafael Swell area.

Red River Gorge in central Kentucky is reputed to have some of the best rock climbing in the world, if you go for that sort of thing. If you don't wish to climb, the area is full of limestone and sandstone formations including a great many natural arches. The most remarkable is Natural Bridge which is a state park. It's also a bit more touristy than the Gorge itself.

They do not mind driving a day or two from Chicago. Southern Utah would be a bit far. Upper Peninsula of Michigan sounds about right.

Shawnee National Forest at the southern tip of Illinois is big, beautiful and peaceful. In various parts of the series of state parks adjacent you can explore waterfalls, unusual rock formations, and take interesting hikes amid huge boulders alongside a creek. Here's a link to one site that has more info. Gorp site page for Shawnee National Forest

I can agree with the above selections, except Utah, as being practical. This would not appeal to e3verybody, but sometime I would like to take a week and just go from one rural state part to another in places like Iowa or Nebraska. Not high profile locations, but All American campgrounds - Lake Anita west of des Moines comes to mind.

Moab, Utah is 19 hours driving from Chicago, so with the OP's 'day or two driving' mandate, it's doable...and absolutely fantastic. Alternately, the mountains in Colorado would be closer, and I imagine there would be a veritable plethora of opportunities.

It's not in the US - but the North shore of Lake Superior. As much as I like Michigan's Upper Penninsula - the rocky cliffs of the north shore change the experience from the rest of the Great Lakes. There are wonderful provincial parks dotted all along the lake and one very nice Canadian National Park.