Mount Greylock State Reservation
There's a lot of great hiking at Greylock, with trails going all over the place. We started at the campground and hiked up to the top of the mountain via the Vista trail, then came back down along part of the Appalachian trail. Later in the day we hiked out to see wreckage from a plane crash, and continued along the loop trail back to the main access road. We also hiked the self-guided nature trail that begins at the south entrance to the park.
This was a great place to come for a weekend's worth of hiking, with several points of natural and historical interest, plus fantastic views from the summit. Greylock has lots of amenities, including a lodge at the summit with food and restrooms, and a strange stone tower with a viewing platform at the top. There's a small museum and lodge at the southern entrance.