I've been through this with a couple of students (my son and a friend.) Many colleges will not accept something like a PO Box. They would accept something like a lot number in a RV park, but quite often you can't get mail there. Any time you have to apply for aid, your address on your FAFSA and other aid forms needs to match the address you use for tax returns, and they all need to match the physical address where you live.
IME attempting to move around in a RV is a not a good idea while you need to stay in a specific area for in-state tuition. You would be better off getting a shared apartment, with regard to utilities and maintenance costs.
Now I realize that rents are sky-high in Austin, and that may be what's moving you towards a RV. If you still decide to go for a RV, my advice is to get one and park it in one place for extended periods. That means a commercial RV park. You can only stay a couple of weeks at most local/state/Federal campgrounds.
