I would make a list of reach schools that give merit: Vanderbilt, Wash U, etc. Keep your expectations in check- getting in without merit is a reach.
Schools like Richmond might be a strong target, but become a reach because you need merit to attend. Same for W&L etc.
Take a look at Lafayette and similar LACs that give merit. Maybe look at Hobart and William Smith, Denison, Rhodes etc.
You would likely do well, merit wise, at honors programs/colleges within state schools- U of SC, Ohio State, etc. Take a look at at Pitt, Maryland and SUNY schools. Some of these schools might fall within budget even without merit.
Apply to Princeton if it is affordable, but again, keep your expectations in check.
Are you thinking premed/prehealth as a possibility?
Good luck!