I am specifically interested in walking/hiking/cycling rather than going to the beach or skiing.
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The Appalachian Trail is a stop on the Metro North Railroad on weekends.
I once did a day trip from NYC to Princeton University, which is not that far away. I really went for the campus, which is really nice (when compared to the 1970s concrete bunkers of my Uni) and also for record shopping. But there are several hiking trails nearby. The Sourland Mountain ones look interesting. I haven't been around in New Jersey that much, but that part of it was actually quite nice.