Virginia is a relatively large and varied state with numerous attractions across its length and breadth. Where you go and what you see will depend on your special interests -- whether you're into history or into hiking, for example. I have suggested a few itineraries that will take you throughout Virginia, to its Colonial-era attractions, its Civil War battlefields, to some of its vineyards, and up the Shenandoah with a little Shakespeare thrown in. I've also suggested how parents can travel with their children in Virginia without going stark raving mad.
Unless you limit yourself to a few major cities, it's best to drive, whether in your own vehicle or a rental. The roads are good and well marked everywhere, even in the mountains, so you should have little difficulty navigating here.