Plenty of those, mostly in Suffolk county. If you like woodlands and ponds nothing beats the pine barrens.
They have some small ponds in Ridge in Brookhaven State Park, plus vast woodlands in the Manorville hills with some really nice overlooks (Bald Hill off Rt.51).
You're probably lucky to come across another person when you're walking in the pines.
For bluffs overlooking the water, check out Wildwood State Park in Wading River, it has absolutely awesome views of the LI Sound and rocky beaches. For views of the ocean from cliffs nothing beats Montauk.
Connetquot State Park, albeit a bit busier, is less of a trip and is in Oakdale off Sunrise Highway, has miles and miles of trails through pine barrens and the scenic connetquot river.
If you really want to see something unusual go to Westhampton by the airport where there are plains of these stunted pitch pines, known as dwarf pines, they are globally rare.
If you take narrow trails you will have to worry about ticks, and the biting pine flies are another headache. I generally prefer Oct-April for hiking in the woods, in summer the ocean beachlands are the place to be, I love Smith Point and Fire Island in general. Another great place is Napeague, where stunted pitch pine trees grow in sand dunes by the ocean.
Here's some photos
view from the bluff over LI Sound:Wildwood State Park
connetquot river, view from bunces bridge, connetquot state park
dwarf pine plains, Westhampton
http://gallery.njpinebarrens.com/data/400/medium/westhampton7.jpg (broken link)
kettle hole pond, Brookhaven state park