“Similar” in what respect(s), other than size?
If all you want are alternatives that are a bit less expensive and selective, then the most obvious are among your own in-state public schools (UMCP, St. Mary’s College of MD, UMBC, etc). Of these, St. Mary’s may be the most similar to W&M (but smaller).
Many private schools might have lower net costs than W&M, but that would depend on your eligibility for need-based aid or merit scholarships. Run the online net price calculators for any schools that interest you. If you think you can’t cover the Expected Family Contributions, then you’ll need merit money (maybe a lot of it). Your stats are high enough to get full tuition at some schools. Depending on how much money you need, you may need to focus on schools outside the USNWR T100 and in locations many students consider (rightly or wrongly) less desirable.
http://automaticfulltuition.yolasite.com/
If you need less than full tuition, look for merit award opportunities in the Kiplinger listings:
https://www.kiplinger.com/tool/college/T014-S001-kiplinger-s-best-values-in-private-colleges/index.php
https://www.kiplinger.com/tool/college/T014-S001-kiplinger-s-best-values-in-private-colleges/index.php?table=lib_arts