When I was there in the early 1990s as an enlisted guy, the best place to live was Virginia Beach area. The crime was fairly low and the place was far enough from the Navy that you could forget about it for a while. Then again, Oceana was close, so it was there if you wanted something. Remember, Va Beach is a resort town as much as a Navy place.
The morning interstate traffic pretty much flows toward the base, and they have a dedicated HOV lane heading into the base (I-564). The traffic reverses in the evening to get home. There are many nice apartments, houses, condos, and townhouses in the city of Virginia Beach to rent.
Someone mentioned Ghent, which is an old Norfolk area and that is nice, too. It has the feel of a college town type area, with lots of small bars and shops about. Old Dominion University is here, so you will get the college age crowd. Ghent is also pretty close to the main Navy base.
Places to stay away from are Portsmouth and Norfolk proper. These places are a bit run down, and some parts had a little gang activity during my time there.
You can call the Navy Family Support Center on one of the bases or the Navy Marine Corps Relief Society to get some detailed info on the area and where the best places to stay would be.
If you have a sponsor at your new command, they would be a great help as well.
Hope this helps.
P.S. I should add that I was in Va Beach this June for my two weeks reserve training, and the neighborhoods pretty much looked the same as when I lived there in the 1990's, so this isn't totally old info.