Kaneohe and Kailua are both beautiful places to live, but so is everywhere else on the island (though you should avoid the western shore if you aren't local). The traffic between Pearl and K-Bay/Kailua can be brutal; I'm talking an hour and a half to go less than ten miles. I lived in Aiea when I was out there, and it could sometimes take 45 minutes to get the three miles from my house to the Sub Base. I'd strongly recommend going to your boat, meeting the folks and moving in with some established people. That will probably find you a good money making deal, and you'll most likely have a reasonable commute.
Remember that you have to be E-5 or E-4 with over four years in the Navy to recieve BAH. If you're not E-5 yet, give it time and you'll make it off the test. Wait until you go to sea a few times before you decide you want two more years in the Navy.
Make sure you take advantage of what MWR offers there. You can learn to surf (lessons were seven bucks when I was there) and snorkel equipment rentals are either free or dirt cheap (I checked out snorkeling stuff enough that I got to keep it). Some of the SCUBA schools there offer great military discounts (and I still kick myself for not getting certified). If you like to go out and drink, hit up Arnold's in Waikiki. It's the only place in the Waikiki area that actually has cheap beer. Remember not to drink and drive, though.
Good luck and have fun!!
EDIT: I take it you're a JO, so disregard the E5/E4 thing. I'd still recommend checking into the BOQ(if you're not married) until you get to know the fellers on the boat. Make money, save drive time. You win!
