Smith's Point on Long Island (exit 64 on L.I.E.) has beach access, trails through the dunes and camping. Since it's a county park, you would need a Suffolk County green key card to get a seasonal pass. But, my friend was in from Boston last year and was able to get a daily pass.
Can't remember what they charged him, but it was a little high compared to what they charge for the season.
It's really nice there and something to look into:
Only Key holders are permitted to make a reservation
There's also Hither Hills in Montauk. Haven't been there yet. It's another County park, so same rules, I would assume.