I, too, know a few people that go there. Like Snowcase said, Gore is probably one of the more popular mountains. Jiminy Peak in MA is a bit over an hour away, and Stratton/Bromley/Magic are all within 2.5 hours, I'd say.
Closest Mtns are Mt Snow, (1 1/2 hours) West (45 min), gore (1 1/2) and all the Catskill mountains like hunter and such. Albany is a great town, I've lived there my whole life (not currently, but I'm only like an hour away). You can ski mt snow all year, and go to west at nights after classes sometimes too.
Im a junior at Siena. Its ok, if I could do it again id go to UVM. I really only ski at Mt snow and Killington, they are a pretty hefty hikes to get to, but a lot of little mountains are closer. Its a ok school, you can get into any bar in albany, classes are pretty sweet. Idk if you get into uvm go their but sienas not to bad, if you have any questions about siena you can pm and if you do go to siena that would be sweet more skiers are always a plus