Chesapeake Bank, the current online bank market leader for rates, is listed by bankrate.com on their safe & soundness rating system as "sound" with four stars. I am in Northern Virginia and have a friend who lives in Williamsburg, VA and he plans on checking into them down there. I plan on switching soon, they also have decent interest rates on their checking (2.5 - 3.25 APY depending upon your balance w/ 1-10k at 2.5% APY, 10-25k at 2.75 % APY & 25k+ at 3.25 % APY.
Here is their homepage:
Chesapeake Bank