Portsmouth is a beautiful area! The whole Chesapeake Bay area is such a wonderful place to live with so many activities for a family. The Navy Base there is fairly large considering it houses the eastern fleet. From everything I have seen of the base, it was quite nice.
I dont know if you will be living in on base housing or accessing area housing with your housing allowance. Not sure what the allowance is there but you can check online on the bases website.
Fishing in that area and boating is wonderful. Va Beach is very close. Not far up the road is Williamsburg, Jamestown and Bush Gardens. About 2 hours from you is the capital city of Richmond and then about 4 hours from you will be Washington Difficult Child. With kids of your kids ages, they will adore living there. I believe you can get military discount passes to Bush Gardens and the nearby water park for the season. It is only like 20 or 30 mins away. The swimming, boating and fishing on the bay is something that would be extremely good for the kids.
I honestly cannot speak highly enough about this area...and no..I dont work for the chamber of commerce there....lol. I grew up in Richmond Va and spent time there. I have also recently vacationed in Portsmouth because of my son who was in the Marines got military hotel vouchers to stay off the Navy base. Lovely side benefits they have...lol.