Get a good Atlas. Look for a National Forest, Park, Recreation Area, Wildlife Refuge, and so on, include State stuff too. Look for something 50 to 200 miles out, generally you will find something quite interesting and surprising. There are a few dead zones and some special (read crowded and hard to get into) that may take preplanning and stops in Walmart parking lots to reach.
We did 16000 miles in 5 months, saw lots of stuff we didn't expect to see, did stuff we never expected to do and found that sometimes good stuff was just a short distance away from the popular stuff (e.g. Red Canyon vs Bryce for just one).
Also found the crowds disappear most places if you go more than a mile from the road
. Pack a lunch and water.
---stan