Damn, I can’t believe I posted my response above 5 (edit: 6*) years ago now.
My family still lives in the area and the Suffolk area I described is still very nice, and again the commute on 664 (Monitor Merrimack bridge) isn’t as terrible as the I-64 HRBT would be. If you want to avoid the tunnels you’d have to do something up on the Peninsula: Newport News, Hampton, or Williamsburg. I’m not as well versed on good areas in the Hampton-Newport News area, but I’m sure there are some. Kiln Creek is nice I’ve heard, but there are also some really sketch areas in Hampton and “Bad Newz”. Williamsburg is very nice but also more expensive and a lot of old people. Norfolk and Virginia Beach probably have the best options for places to live, plus schools, but I think the commute through the tunnel on I-64 would be hell every day. Plenty of people do it though.
There is a pretty large amount of private school options. Nansmond-Suffolk is in Suffolk, Hampton Roads Academy is in Newport News, and Walsingham Academy is in Williamsburg. There are even more in Norfolk and Virginia Beach. Look up TCIS Conference and you’ll get a list of all of them.
Feel free to PM me if you have more questions. I actually went to one of the private schools in the area from 1st-12th grade back in the day.