Lots of boarding school kids go to Georgetown (popular choice) but I wouldn’t say it is boarding school like other than being a little preppy.
I would suggest the previously mentioned Trinity, Middlebury, Bates, Bowdoin, Colby - pretty much the NESCAC colleges. https://www.nescac.com/about/members
Also, small to medium sized schools like Davidson, Richmond, Wake Forest to name a few.