"Cousins" are welcome here! It sounds like your travels will be fun! Are you planning on traveling through New Mexico, Arizona and Nevada, or trying to choose between the three?
There are many threads on nice places to stay. Bob Thompson has a nice list that is fairly useful as you travel and need a place to stay overnight! Here is a short list of his:
There are also many sites for state parks. I suggest you google each state you are interested in for "Nevada State parks" , etc. and you should get the official state park information. Most seem to have detailed information about what there is to see, when they are open [many close during winter in the north, don't know about the south] prices, trailer length, etc.
Good luck and have fun!
Mrs. NorCal Bambi (traveling in S Tardis)