- Outer Banks are nice - as said here, see the Wright site. There's a Visitors Center but it's not really a museum. But they've really preserved the dunes and beach. Nags Head is the big stop on the OB - expect it to be crowded in the summer. You're close enough to Roanoke (Ft. Raleigh) to check it out since you're there. Not a lot to see but fascinating anyway.
- Williamsburg is cool but if you're not into the history, it's kind of boring. But I'm a history buff, so I always liked it. I also really liked Jamestown maybe even more, it's eye-opening to see the conditions they lived in, but again not a lot for non-history buffs after a few glances.
- Montecello is great as is UVa. Do them. There are also quite a few wineries within a few minutes' drive of Montecello if interested.
- Shenandoah NP - very nice, but keep in mind it's a camp/hiking park, so by car it can get old after an hour or two. If you're going up 64 from C-Ville, take the U.S. 250 exit into the park (north is Skyline Drive, South is Blue Ridge Parkway - same road, different names at that point). Once you're in, the next access out is U.S. 33, about 30 miles up the road. Take it if the family has seen enough - the next egress road is U.S. 211 - about 40 more miles. The drive can have traffic and is a little wind-ey... most of the length of the park is the same essential views across the valley, which are all nice - but you don't need more unless you camp/hike (IMHO).
- Richmond - nothing there really.
- D.C. way too much to talk about, but obviously if first time do all the "tourist things" - historical/political sites, museums. It'll be humid and fairly crowded. You mentioned Alexandria, very nice town, worth a stop, especially the older part down near the harbor. Other than that I'd have 35 paragraphs on how to do D.C. Way too much here, ask if you want specifics.
- I-81 is just as bad as I-95 - maybe even moreso, as it's very crowded (more traffic than 95!) and essentially a 4-lane highway. LOADED with semis, trailers, etc. Hilly and a lot of cars in the summer = tension. I'd turn right on 33 out of the park (not left to get to I-81) to get U.S. 29 (about 15 mi.) and go to D.C. that way. Very pretty, a bit slower granted (but not that much!) and not nearly the traffic.
If you've laid out 8+ days for your loop, that's pretty good. Any less and you'll be pushing it. That's a lot of miles driving (more than you'd think) and a few of those places really aren't good overnight destinations. But it should be nice. Starts getting humid about late June and man it can be a sweaty armpit if not used to it. Take talc or whatever doesn't cause cancer nowadays. Good luck, we're all counting on you.