As a parent of a recent Physics grad from Dartmouth, just wanted to add a few things. My son looked at all three schools that you mention, ultimately applied ED to Dartmouth and he was very happy with his choice. He thought Cornell was too big and Williams too small, at least for him. He really wanted a LAC environment, wanted to major in Physics but be able to explore engineering. Cornell required an application to one school or another (A&S or Engineering) and though you certainly take courses throughout the university, changing majors can be a challenge. Williams of course, doesn’t have engineering.
His professors gave him a lot of encouragement and 1:1 time, he was involved in research from his second year (could have been sooner if he had wanted to), and was closely mentored in his thesis project. He is now in a PhD physics program and feels that he was very well prepared for it. He is still in touch with several Dart profs.
As far as social life, etc., he was not in a fraternity, was not a drinker particularly. Some of his friends were in frats. Students seem to go to parties if they are interested regardless of whether they go Greek. He had plenty to do, was involved in the Outing Club and some organizations focusing on world issues. He loved Hanover and was sad to leave, though happy where he is now.
Oh and study abroad options were great (they probably are at all three), and D plan offered flexibility and options.
Congrats on your fine choices and good luck with your decision!!