charley
I would apply to both and see who gets you in first. I think both have coordinators who work with patients to find housing. There are 2 military RV parks here and some stay at Flagmingo RV Park north of town. Those staying there like it. I pay approximately $100 week here at NAS JAX and I believe Flamingo is $600 month. I have heard housing is 1000 month and up but most seem to find places.
For Florida call (904)588-1800, or toll free (877)686-6009 that will be the switch board. Ask to speak to Katie Mahoney. She has housing information. No information on Bloomington but look them up on the net and call.
Richard