Based on your updated info, definitely check out William and Mary (W&M), Holy Cross, and Lafayette. All top-notch academics. I think W&M is a bit of a hidden gem for international students. It’s a mid-size national university, second oldest US university (to Harvard). Retains “College” in the name for historical purposes but a public university ranked with Michigan, UNC, Cal-Berkeley, etc. in public university rankings, but not nearly so many international applicants. Big thumbs up from me on Holy Cross too.
And Wellesley and Smith (smaller but neat town) if female. It sounds like Dickinson and Hamilton would be a little too isolated. Richmond might be too Greek, and maybe too southern preppy.
Some other ideas,
University of Vermont–smaller state flagship, more of a mid-size university with something of a LAC vibe; extremely cold but great for outdoors activities (hiking, skiing, mountains); adjacent to Burlington, a great town, with Church Street, a pedestrian nightlife area, right on Lake Champlain (a very large lake), with beautiful sunsets over the NY Adirondack Mountains to the west.
University of Cincinnati–a bigger school, good urban option, in a nice city.
University of Pittsburgh–a bigger school, good economics and a med school, in a city with lots to do, and very near Carnegie Mellon University
Good luck!