Tufts is a good suggestion - it’s a small university with an LAC feel, its Medford/Somerville neighborhood is definitely urban, and getting into downtown Boston is easy on public transit. It has both a competitive ski team and a recreational ski club, as well as an active Mountain Club with its own lodge (called The Loj) that organizes backcountry, telemark, and x-country ski trips as well as downhill. They have a club equestrian team as well. Excellent medical care in Boston, obviously. Solid student services - admin has its act together; they’ve mounted one of the most proactive and successful pandemic plans of any urban school. They have both a traditional psychology department, and an engineering psychology major that focuses on human factors in tech. Study Abroad is huge, and they have also sent ASL students on exchange to Gallaudet University in DC. Tufts has ED2 which would improve your odds of acceptance.
Boston College deserves a look too. BU has the kind of setting you want, and a great psych department - just not so much the intimate LAC experience… but if you apply to the Kilachand Honors College, that might strike the right “best of both worlds” balance.
Have you considered Clark as a safety? Psychology is the major they’re most known for - it’s the only US university where Freud lectured - their Freud statue is a landmark. 2300 undergrads on an urban campus in Worcester, MA (home of UMass Medical Center), and it’s an easy 45 minute commuter rail ride into Boston. It has an equestrian club team, and an Outing Club which has merged with the Ski/Snowboard club, and sponsors many ski outings. It has an active Prism group and a student-run EMS program. Also a robust study abroad program. Holy Cross, also in Worcester, is worth a look as well - internships with fieldwork are a strong component of their psych program. Campus is a little more removed from urban Worcester than Clark’s but still in the city. There’s cross-registration between the two, as well as WPI and others.
Emory is another small LAC-like university in a major city, that has EDII. Ski trips are only a thing on breaks, as you’d imagine, but they have a top-notch equestrian program. They offer both a BA and a BS in psychology. The University Hospital is top-tier. Atlanta is an amazing city with an active LBGT community, and the university itself has strong LGBT activism as well. Excellent speech & debate too.
As others have said, Fordham might be a good fit as well, if New York is your favorite city. There’s also Eugene Lang College of The New School, which has a dual BA/MA program.
As a Scripps parent, I agree that Claremont probably isn’t what you’re looking for, setting-wise, although it would be great academically.
Good luck, and sorry for the disappointment with Barnard. This is a tough year to be applying - so many factors are making results even more unpredictable than usual.