4 months is a good amount of time. I think a lot will depend on your budget.
The " American Rockies" covers a lot of territory as does Yosemite and Yellowstone.

What do you want to actually DO in any of these places? whitewater rafting? Amtrac train? museums? You left out Sedona/Flagstaff/Las Vegas where you could spend a couple of weeks just seeing the ruins and hiking the Grand Canyon.

I think you need to research each area you are interested in. See what activities you want to do in that area. Then start narrowing down a trip.

I am not sure if you can buy a car in your first place and get insurance to cover the trip. Then sell it at the end. This would give you the freedom to backtrack if you want, spend a week here or there or just keep going.

The one place I would not buy a car is California. California has some funny rules about becoming a tax resident for the State.