I've always enjoyed pocketing my BAH but if the on base housing looks decent during school I might bite for the convenience.. depending on where I head for intermediate/advanced.
If they wait is long enough in Pensacola I might even check out what's for sale.. could make a decent rental after leaving.
Pensacola isn't as affordable as it used to be, doubly so when you add in higher interest rates. Also managing multiple tenants with differing lease end points can be an ongoing pain in the ass.