I did an internship at the La Jolla Playhouse years back, and they did offer housing. They didn't pay, but they did reimburse me for mileage too. I don't know if they still do, but if you want to get really far away from the East Coast, that's pretty far.
I wouldn't give up on getting non Eq. Assistant and PA jobs that pay enough to pay rent. My last PA job was at another LORT, and I had no problem paying rent with about a week of work, health benefits, parking, overtime, and a season contract. It's not get rich money, but I wasn't broke, so it was worth the move. Those kinds of jobs come around every once in a while. I'd look at ARtsearch.