About 35 minutes in on Long Island, Connetquot State Park is a large and secluded park and perfect for an early hike. The trails are flat and therefore relatively easy, but the sand is loose for horses, so there is some added exercise to walk on it.
At the entrance stand three absolutely gorgeous art and craft style buildings and a long serene pond with swans and geese. The trails vary in length from 2 miles to over eight. They have a trout hatchery which looks cool from the brochure, but to be honest we missed to turn off to it twice and had walked several hours and didn't feel like trying a third time.
Overall a lovely, peaceful place where you are unlikely to see more people than geese.