People tend to check in during these times:
There is an awesome view of West Point across the Hudson River if you are waiting on track 2.
Enjoy the views!
Elevators always smell like piss.
Bring back the pub and store at Guinan's!
If you just miss catching the train on a weekend, like I did, you can while away the hour-long wait by hiking in the adjacent state park (trailhead is at south entrance to parking lot).
If you are going to West Point use the ferry across the river. It is $.5 and goes faster than a taxi. ( only works from April to October).
Park at S end of lot and find sign marked Arden Point btw stone pillars. This is Arden Point & Marcia's Mile trails.