You must have reservations at RV parks for the July 4th weekend anywhere near big cities and in National Parks.
Do you really need to start and end your trip in LA? You probably know what a nightmare the traffic is there. And guess what, around holidays is even worse. Maybe start and end in Phoenix instead. Head north to Flagstaff and visit a really cool ancient cliff dwelling town, than visit Meteor Crater. Death Valley in June would be horribly hot, most wouldn't even consider it. Maybe visit Lake Tahoe, then head over to visit Virginia City where Mark Twain wrote for the newspaper. From there, there are so many choices in every direction it'll make your head swim.