The Pine Barrens are close maybe 2-3 hours away. Byre State Park and Wharton State Park have trails where you can see carnivorous plants in their natural habitat. Wharton is larger and has more trails, check out the Atsion Lake campsite area. elgecko (Steve) has some great pics on some of his pine barren trips (9 so far) he has posted here. There's also the infamous Jersey shore. Point Pleasant and Seaside Heights about 2 -2.5 hrs from NYC have boardwalks with all the food and game stands. Sandy Hook is much closer (45 min from NYC) is a Nat'l Park(Gateway Nat'l Park) that has some seaside wildlife areas and swimming areas.
there is a pleasure in being mad, which only a madman can enjoy!
I'd second quogue's recommendation of checking out the NYBG or Brooklyn Botanical Gardens. Not much in terms of CP's, but still sites to see for sure. Gorgeous grounds in the heart of millions of people! And being so close to NYC, it'd be quite the easy trip!
I've heard great things about the NJ Pine Barrens from RL3786, but its vast land for sure....
I've also heard wonderful things about the Long Island Pine Barrens which would probably be about a 2hr trip or so and I'd imagine it isnt as vast as NJ considering its size, so easier to explore.... lots of drosera and sarrs from what I've researched.... shame I haven't explored myself to be honest....
Good luck with your brief visit
2 hours north of the city is FDR's house and Eleanor's Valkill. Also the Vanderbilt mansion, The Sam Morse estate. Further north is the Mills Mansion. All on U.S. Rt. 9
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