Go to Amherst undergrad. You’ll get so much more attention and mentoring.9 majors: 9 profs+ tons of undergrad research opportunities! I honestly think you’d be crazy not to go to Amherst. You can take engineering at Umass thru the consortium, and it’s a 5 minute bus ride away. You also can eat there when taking a class, and there will be hundreds of people from your country, whatever it is, that you can reach out to if you don’t find your social niche at Amherst.
Haverford also has a consortium, and you can get classes at UPenn or Swat, tho further away and harder to arrange. I’d ditch Williams.
Amherst is a fabulous gift and you should take it. Don’t look back!