Are you single? Do you have pets? Kids?
We lived on base for a few reasons:
1. We had just gotten married a month before we went to Japan and I knew nothing about the Navy, Japan or anything else...it was the easiest option.
2. We had cats...we knew people that lived off base with cats, but we didn't want to have to worry about ours destroying tatami rooms and paper doors. We also wanted the built in network of having people who would be willing to watch them if we went away traveling. And, we completed the quarantine in our on base housing...something we couldn't do if living out in town. They would of had to been quarantined in the Zama kennel.
3. Convenience. I liked being able to walk to the commissary, the NEX and the post office. I also liked that when I got home from work later at night I could walk out my door, and go running/biking around base at 2300-0000 safely (no cars, people, etc to worry about).
We didn't like how small it was though, everyone knew your business and you lived close to those who you sometimes wanted to get away from.
We've been talking about it recently and if we were to go back (we want to), we would probably live on base again. Only now our reasons have changed slightly since we're expecting our first kid.
There were probably half and half single guys in our squadron that lived on base/out in town. We had 2 that shared a place in Atsugi area and also had a place up in Tokyo, which if I were single I think would be the perfect set up if you can swing it.
I don't know how much you're going to be gone, but the amount my husband was gone the only thing I could see with living out in town is that most of the time (3/4 of our 2.8 years out there he was gone) you're not using what you're paying for. At least if you live at the Q you've got maid service, and all that jazz and you don't have to go far when you come back into town (or when you're drinking at the O-club...since it's right there).
Hope that helps, we've been back almost a year now and are already talking how we can go back. If you need any info on things to see, we got off the beaten track a lot, so feel free to ask.