As a Virginia resident, you can apply to Virginia Tech and hope to receive one of the scholarships that would make it affordable. Also, I don’t know if I can persuade you, since there is a big rivalry, but the University of Virginia meets full need. It could be a more affordable option for you.
If you can get your SAT/ACT score a bit higher, you may also want to look into applying to colleges through QuestBridge. Their general guidelines include an SAT >1310 and/or an ACT >28.