Welcome to the RTA Forum!
First, if you are looking for a Euro-style campervan, you'll find they are quite rare in the US, especially on the rental market. There are a couple of places that offer them, but the vast majority of the market offers the larger RVs.
Also note that an RV or campervan is almost certainly going to be more expensive than renting a car and staying in motels. Also know that since you are under 25, you could be looking at fees of more than $25 per day, per driver, on top of the normal car/rv rental fees.
As far as where to go, that really has to be something you decide with your friends. A few options would be to go through Death Valley, Yosemite, San Francisco and the Coast. Or visit some of the National Parks in Utah, down to the Grand Canyon and back to LA. Or a loop around Arizona, including the Grand Canyon, Phoenix/Tucson, and San Diego.
There's lots of threads about those kinds of trips on this forum, as many other resources here to take advantage of, to help you come up with a plan.