I was stationed out there for 4 years with the Navy. You get BAH on base but the housing contractor takes it all back. What you do get is your left over utility allowance if you’re under at the end of month (usually doesn’t happen if you like to have air conditioning). Look at the cost of living allowance calculator as well that’s your extra take home.
When I was there as an O3 I was living out in town collecting $3600 a month in BAH and another $1200 in COLA. Both have gone down considerably since.