Out West this time of year, get yourself a bear bag, plenty of rope to hang it, and bear spray with holster. It can be expensive ($80-100) but worth it and often required to camp.
Also, "Up and Off the Mountain by 2:00PM" is a good rule to avoid lightning at elevation.

Yellowstone NP, WY -- Park has entrances at roughly "N, S, E, W" directions. From South Dakota you'd be on RTE 14 toward West entrance and hit Cody, WY. In Cody, WY, the Buffalo Bill Museum has an incredible firearms and art collection. Town of Cody is ok for lunch...
From Cody, Head West towards Yellowstone, you can Camp off the road in the campgrounds throughout Shoshone National Forest. It's beautiful and cheap for overnight sites, and there are many "ranches" along the road you could look into if you want to fish and ride or eat. The Yellowstone gate from Shoshone is burnt and all uphill.

Yellowstone is luxurious in the northern half. Lodge food is great, camp sites are nice, and the big animals are very active in the valleys up there.

Sulphur Springs and the overlooks like Artist Point are worth the walk from the parking lot.
I believe you can hike all the way to the river at Lower Lookout Point and have yourself a secluded spot along wide river banks.
Firehole River has a swim area.

You could take some of the hiking trails available to you in the North like Specimen Ridge (Just past Roosevelt Lodge). Gas station at Roosevelt Lodge has a hot-water tank inside which is nice for meals.

Yellowstone, FARTHER NORTH: If you're feeling crazy, the scenery on the drive North (it's a long one) to Cooke City/Silver Gate is really beautiful and along Beartooth Hwy (212), and there is a weird "big" little town at Cooke City with a restaurant called Log Cabin Cafe, expensive but really good pancakes.

Joshua Tree, CA....is a desert. Get a date shake and go.

Big Bear Lake, CA is about 100 miles northwest and has very pretty alpine setting but weather can be an issue with mandatory chains and 4wd use on some trails.