Buffalo doesn't have top 25 schools like say Chicago or Pittsburgh
but
UB (the largest of SUNY-State University of NY) is rated #
89 for National Universities (both private and public), and #
38 in Top Public schools.
On the world ranking it's an internationally recognized school at #286. UB is also one of the oldest medical schools in the nation (1846) which built a new $375M campus downtown in the Buffalo-Niagara Medical campus.
https://www.usnews.com/best-colleges/rankings/buffalo

UB Jacobs School of Medicine and Biomedical Sciences built on top of the Metro Rail (light rail) station at the end of Allen St ("Allentown")
Students can live a great scholastic life with plenty of parks, arts and culturals, professional sports, bars/restaurants. Go Bike Buffalo is constantly pressuring the city to build more bike lane infrastructure as well. The only downside is that since Buffalo is growing again you can't find large, "sweet" 1 bedroom student apartments for $600/month anymore but with a couple of roommates you can find spacious apartments in great neighborhoods (Allentown, Elmwood Village, North Buffalo) for not too much per student
There's also:
D'Youville University (top 300)
Buffalo State College (UB's little bro)
Niagara University
Canisius College (Jesuit institution)
Daemen University
Medaille College
Villa Maria College
Hilbert College
Approximately
40,000 undergrad students total. Not sure the grad student count, but considerably less.
and for 2 year community/technical colleges: SUNY Erie Community College across 3 campuses