Never biked on the skyline drive, but I've heard from some who have that the narrow roads can be a problem. Try the Shenandoah Valley, similar views (from the other direction) and ok roads.

Have ridden the Colonial Parkway. Pleasant enough, but not challenging. Good start for a day of biking around Williamsburgh. Tends to be buggy in summer. The drivers on the parkway are usually well behaved, but can get impatient when the passing lane isn't available.