Actually, I think Virginia is a bit more distinct than your tiering system with W&M though your overall tier is pretty spot on.
I believe Virginia and California are the only States to have two Public Ivies. In Virginia, it's UVA and W&M. I think it may also apply to the top 35 ranked by US News. So yes a legacy is ok coupled with VMI though it sells W&M a bit short in my view.
I would probably link UR and VMI as the legacy schools. W&M would be better tagged as the Public Ivy. UVA as the flagship is also correct.
The other area dismissed here are the more academic D3 schools in VA. They would include Washington & Lee, Randolph Macon, Hampden Sydney and Emory and Henry. They are considered a breed apart from Christopher Newport and Mary Washington.
Lastly, there are notable women's colleges such as Sweet Briar and Mary Baldwin.
You forgot the cherry on top of the sundae that is Virginia ... Liberty.