Virginia to Maryland
 

I presume you are going south to Norfolk and then across the bridge to Maryland. I don't know about quaint towns, but there is a maritime museum in Norfolk that has a lot about history of seafaring, etc., and there is an old battleship there also which was the biggest one the Navy had, or something like that (USS Wisconsin). I don't think there are that many historical sites of interest in that part of Maryland, they are on the other part of the state in southern Maryland across the bay.

Up to you, but I would use the Bay Bridge Tunnel and travel northward to Easton using US 13 and then perhaps Rte 50. There are several possibilities further up the Shore closer to Easton including what you might, or might not, consider to be a "quaint" town such as Berlin, MD. Am sure somebody is going to rave about St. Michaels and perhaps even Chestertown and Chincoteaqgue

It is unfortunate that you do not say where your required starting and ending points are which would be very helpful with routing recs.

I agree with Dukey (although we did the trip in reverse, taking the Bay Bridge Tunnel from the peninsula to the mainland). We stayed in Chestertown several times and enjoyed visiting Chincoteague (my late husband had a cousin who was a preacher there) and more interesting seeing the wild ponies at nearby Assateague.

Although the route over the Bay Bridge Tunnel is the logical one you could also go across the York River and take routes 17 and 301 on the western side of the Chesapeake Bay. We took that route from the DC area to Williamsburg a few years ago. We detoured along the Potomac and stopped at Stratford Hall (home of the Lee family) which is an interesting historic site. The George Washington Birthplace historic site is very near and there are lots of vineyards and other places to visit.
I am not sure whether you are going RT Easton to Newport News but if you are you could certainly take this route one way.

My husband and I are planning a trip to the Eastern Shore next fall and definitely want to visit the new-ish Harriet Tubman Underground Railroad National Historic Park in Cambridge, about half an hour south of Easton.
https://www.nps.gov/hatu/planyourvisit/directions.htm

I suspect with a week to drive a relatively short distance, the shortest route isn't what you necessarily have in mind. It would be useful to have clarification on that point & to know if you've visited the area to know where you've already been.

To me the obvious wealth of possibilities is Williamsburg & the James River Plantations.
https://www.nationalgeographic.com/t...nia-road-trip/

Or on a more northerly path, the Northern Neck, the land between the Potomac & Rappahannock Rivers. With more information we can get more specific.

Easton has lots to see--you might fill up your week there! Centreville and Chestertown also on the Shore, Annapolis (across the Bay Bridge). The Wildlife Festival in Easton gets pretty busy so do check that its early November dates don't conflict (and book early!). Other sweet towns near Easton are St. Michaels and Oxford.

St Michaels for sure Dukey.

If you do come through the bridge/tunnel, Yes, Chincoteague is nice.

Chincoteague for sure