I suspect the OP will be a strong candidate for all the Virginia schools. UVA is always tough so no guarantee, but I’d say it’s a hard target. Virginia Tech engineering is a match to likely, although they are sometimes a little weird with yield protection. VT is not generous with aid, but you should still be under $35k (we’re paying about $33k per year as a full pay family).
The advice to broaden your search to other schools out of state is good, if you intend to engineering. As mentioned, there are a lot of good engineering schools with decent merit and financial aid packages (Alabama and UA-Huntsville, ASU, etc).