My understanding is people in IR think this Foreign Policy list is a pretty good starting point for narrowing down undergraduate options:
The NE/NY LACs on the list include Williams, Middlebury, Wellesley (not applicable), Amherst, and Vassar.
Based on the other things you wrote, I also immediately thought of Vassar. Not that you should rule out the others, but Vassar isn’t a NESCAC school and I understand it to be generally less athletics-focused. My understanding is it has also long been particularly known for being LGBTQ friendly, although at this point I think that is basically universal among these LACs. Still, Vassar made this top 25 list, for example:
By the way, any chance of looking outside NE/NY? Like, just cross-referencing the IR list and the LGBTQ list, I also see Macalester. From what I know that also seems like a good fit in general, and it is in a great city.