So first, William & Mary is very special. Not at all like most publics, really much more like a private, and a very nice one in fact for the right sort of kid. So you are very fortunate to have that as an in-state option, and there is nothing wrong with recognizing it.
It is so special in fact it is indeed hard to find non-Reachy competitors, particularly if you want to stay close to VA and also are not interested in LACs (in many ways the W&M experience is actually more like an LAC than a large public).
I agree Rochester is a good suggestion, but is it close enough? Up to you.
Some other ideas. Pitt and Delaware are actually nominal publics with a similar history. They are very old (although not as old as W&M!), and were not originally publics but affiliated later. And I think they can still feel different as a result. Of course they have all sorts of kids, but you can find your people, and it wouldn’t hurt if you got into their Honors programs.
And actually, Rutgers is yet another of these, with an excellent Honors program.
Another idea would be UNC Asheville. This is a public LAC, so may or may not be of interest, but again it is pretty special. Miami of Ohio is yet another idea, and closer to Virginia than some may realize. College of Charleston too.
But we are getting farther than Rochester now. So again, up to you.