I was there twice, once for a game. Probabaly 2005/2007 timeframe. It is one of my favorite places in the country. A beautiful place, the history that has taken place there with the chain across the Hudson to block the British. The dedication and commitment those kids sign up for. I really liked it there.
When I was there wasn't much to do or see outside the gates. The visitors center is good. There is also a military museum next to the visitor's center. Those are both outside the gates.
Over 10 years ago, they did not allow people to freely walk around the academy grounds. If that is still the case taking a tour is a must. You should inquire about the tour schedule, I do not know if they do tours on gameday. If not and you are in the area Friday or Sunday you should definitely plan on a tour. It will take you by bus around the grounds and stop so you can get out at a couple spots.