My favorite spots for short hikes, and a couple for longer:

1. Mt Holly Sanctuary (Nature Conservancy) and Yarrow Preserve (adjacent to each other). Probably doing all trails in both can be a nice long hike. Westchester County, near Katonah. Edit to add: also the Zofnass Family Preserve and the adjacent preserve together have a good 10+ miles of trails. Also in that general area!
2. Hardscrabble Wilderness near Pleasantville. Park per Google maps. Not a long hike but longer if you try doing all the trails. For nearby or long flat hikes the OCATT!
3. Lots of trails near the Hudson near Haverstraw. I parked on the opposite side of Rt 9 and crossed over to avoid crowds.
4. In NJ not far: Osio Overlook. Parking gets busy though, especially weekends. Very hilly!
5. Stewart State Forest for flatter trails but lots of them!
6. Bigger longer hikes in Harriman on the Island Pond side which is partly Appalachian Trail. I park here:

A good way to find hikes is to join Geocaching, there are a lot of caches set for circular hikes all over the tri-state area. That brought me to the beautiful Saugatuck Trail out near Westport CT which I loved.
Happy Trails!