You single or married? What's your social life like? Have buddies from OCS coming down too? I'll run down what I've seen people do including myself.
Perdido Key: Highrise condos and vacation homes people want to rent. 4 decent bars and the beach nearby, hopefully walkable. Generally more money as you pay the "Beach Tax". A lot of single dudes will get a 3br place with roommates from their commissioning source. 15-20min drive to NASC/Sherman depending on traffic.
NASP Back Gate: Apartment complexes and some bigger houses. Don't stray too far as it get's pretty redneck quickly. Closer to base (10-15min drive to NASC/Sherman), but farther away from social things. You'll be driving to either Perdido or downtown for bars/food. The apartment complexes tend to be more expensive.
NASP Main Gate: Very hit or miss. I lucked out with an okay neighborhood. Small apartment buildings and houses, but good deals. 15 mins to downtown, 10 to NASC/Sherman, 15 to Perdido, 20 to Pensacola Beach. About the middle of everything fun, but close to work.
Downtown Pensacola: Close to downtown (duh), about 15 to NASC/Sherman, 15 to Pensacola Beach. Gets nicer/more expensive the closer you are to city center and south. Some nice historical districts that are good as well. Downtown nightlife is close, hopefully walkable.
Gulf Breeze/Pensacola Beach: Similar to Perdido, you're paying extra $$ to be near the beach. Lots of bars/restaurants here and the beach obviously. 20-25 mins to NASC/Sherman, 15 to downtown.
Cordova Mall-ish: Close to the mall, and the restaurants there. That's about it. Most people up here are splitting the distance between Whiting and PCola because they're married SNAs. No reason to live up here as a SNFO, especially if you're single.
If I had to do it again, I'd live downtown. I kick myself every time I take a $20 cab ride home from downtown, when I could've lived right there and stumbled 5 minutes home. You'll go to the beach during the day, probably with friends, so getting home isn't as much of an issue than at night. You'll notice I put a lot of emphasis on driving times, as you'll be driving EVERYWHERE. Literally nothing is close to anything here and the roads in and around NASP suck for moving quickly. Don't waste 1.5-2 hours a day in a car.