You will have plenty on your plate before you ever think about going away to party anywhere.
However, that being said, I do recognize that as a positive thinker you expect to survive Beast and become a member of the Corps, and that you are wondering what your life may be like thereafter on the social front.
I never went to Penn State to party, and I don't know of anyone who did. That doesn't mean it didn't happen. But it's a long way from West Point. You're looking at a good 4.5 to 5 hours, longer on a Friday with traffic.
You will likely find, as I did, that you will go where your friends have connections or where you yourself have connections. I was fortunate to have a roommate from Connecticut, and he often had us over for weekends when we were able to get pass (as a plebe, that amounted to twice, as we both got a tongue-in-cheek performance pass for an event that shall go unnamed). When I was a cow, my sister was an undergrad at Yale, so we went there fairly often. As a firstie, I went to Albany and Philadelphia with friends as well.
But, for the most part, I became quite the denizen of NYC and to this day count it as my second city home. It's very accessible and, with the right friends who are willing to combine financial forces, very affordable as well. Plus, if you're a young man or gal of considerable charm you may just find a friend of the opposite sex with whom you might start a relationship, which will lead to both easy accomadations and a reason to visit. Several of my friends married lovely gals from NYU and Columbia.
Cadets were also known to frequent various SUNYs, Marist College, and for the politically daring, Vassar College.
Of course, that was back in the dark ages
. Your mileage may vary.