I'd say live off base, even if you're a pilot. I've been in A-pool for 6 months already and haven't even started API. If you have to complete IFS, that extends your stay close to 2 months (unless you go to Eglin and get Mr. Miles who puts you through in about 2-3 weeks).
Unless you have follow-on orders to whiting, you're going to be going to corpus. It doesn't matter if you're married, bought a house, and just had 3 kids start school...unless you have follow-on orders they're sending just about everyone to corpus, which I hear is likely to continue for at least another 6 months.
Most any apartment complex in town is going to have experience with military, so moving out early isn't much of a problem. Just ask.
I'd say live around hwy 98 (Fairfield lakes, Crystal lake), which puts you close to the exchange/commissary, and you're still a reasonable distance from NASC and restaurants, movies, stores, bars, etc.
If you do have follow-on orders, you might look at getting a place along University Ave or Davis Hwy (Eaton Square, Governors Gate, Kings Mill, Oakley, Colonial Village), so you can stay in the same place for API/Primary and not move.
On-base is great for getting to work and not worrying about rent/utilities, but sucks for most everything else. I say get a roommate and an apartment out in town, make some money off BAH, and enjoy your time in Pcola.