I was a Hospital Corpsman in Yokohama, Japan for about 4 years during the late 90's. I worked at a branch clinic that was attached to Naval Hospial Yokosuka. I'm sure the hospital and base have probably changed a lot since then, but I consider it to be one of the best times of my life. I'm starting a BSN program this fall, and I'm really considering joining the nurse corps so that I might have a chance to be stationed there again.
Yokosuka is a fairly large base, with several amenities. Back then, there was a commisary the size of a large grocery store here in the states. There was also a McDonalds, Taco Bell, and a Popeyes Chicken on base, as well as several other more nicer places. There was a good size library, a car dealership, a large gym.... Yokosuka is really like a self contained little city. I have known several people who were stationed there for a year or more and never once left base. But, if you do go to Yokosuka, I would recommend getting off base as much as possible. There are a lot of cool places to visit withing an hours train ride, such as Kamakura, Yokohama, etc.
But, since you have a son who may be starting middle school soon, I would think about going to NAS Atsugi, if you can get orders to there. Atsugi is a smaller base about an hour from Yokosuka, and it also has a lot of amenities. From what I have heard, however, the schools
at Atsugi are much better then at Yokosuka.
Anyhow, good luck to you.