Be warned once you get off the freeway most roads are two lane blacktops.
Plan your trip. Then see what is on the way.
Use Google maps to explore your routes (if you have google earth with 3D you can get a realistic idea of what the terrain looks like (some is not RV friendly).
Walmart is good about people parking RV overnight for free.
Plan your trip, but leave wiggle room for unexpected stops. May just be an interesting road side attraction or a mechanical problem
Monument valley is worth a visit. This was one of our families all time top places we visited (they have 4 hour guide tours which pretty much shows you everything).
Four corners is interesting but it is not on the way to anything, so you really have to go out of your way to get there.
Yellowstone is worth a drive through (unless you made reservations long in advance you will not be able to stay in the park).
Grand Canyon, either the North Rim or South Rim. Most go to the South Rim, easier to get to and more facilities. North Rim is nice but but a long way from civilization.
I would skip Las Vegas, overrated and expensive.
If leaving from Southern California you can pick up a bit of the old Route 66, there are places the road still exist. Good photo ops.
And last but not least, it is going to cost more than you budgeted.