I live about an hour north of New York City and there are many famous things to see around here (obviously). One that doesn't get a lot of mention is the NY Botanical Gardens. It's a really beautiful place, and also has the last old-growth forest in NYC.
Further north, for the luxury lovers among us is the Mohonk Mountain House:
Even if you're not staying in the hotel, the parkland around it is beautiful in all times of the year.
Someone earlier mentioned that they wanted to visit the Grand Tetons. I highly recommend it; especially if you're into backpacking since the views inside the range are even more impressive.