A few that come to mind that aren't too crowded are:
- Walnut Canyon National Monument near Flagstaff, AZ. It's got some amazing cliff dwellings and views into the canyon. Pretty easy to access off I-17.
- Montezuma Castle National Monument near Camp Verde, AZ. You can check out a well-preserved cliff dwelling from the Sinagua people. It's a quick stop if you're in the Verde Valley area.
- Salt River Bay National Historical Park and Ecological Preserve in the US Virgin Islands. It feels very remote and you'll likely have the place to yourself. Nice for snorkeling too.
Hope this helps give you a few more options to check out!