Oh my gosh your daughter sounds like she would be happy at a lot of schools but NMH ticks off everything on your wishlist. My daughter was class of 2016 and at that time the Volley Ball coach was known for being particularly warm and wonderful and while the team is competitive, you do not need to be a recruit to play (unlike hockey and some other sports). It is the size you are looking for, more progressive, friendly and relaxed than many of the schools frequently mentioned here, and it is 30% international. Very little pretension in marked contrast to some of the others you listed. In fact, Northfield was founded many moons ago as a place for indigent students who could not afford boarding schools. NMH also recently started a special program for social entrepreneurs and they have wonderful social justicey type programs. My daughter who was very involved with diversity and LGBTQ issues at NMH got what I would consider comparable to a college education in these topics. The kids were involved in very meaningful work way beyond typical key club stuff. While not every student at NMH is a stem whiz, they can certainly challenge the mathletes etc. among them and they are in the process of creating a state of the art new math/science center (not sure if it is under construction yet) My daughter is a senior in college now but I still miss NMH. Truly a wonderful school (and I am a Taft grad) and they regularly churn out wonderful writers. They do not have as much FA to offer as PEA but they are generous with what they have.