Another vote for Kykuit. The estate of John D. Rockerfeller is over 3000 acres, and a wonderful place to stroll, especially in October. It overlooks the Hudson River, about 25 miles north of NYC.
If you go up to Peekskill, you can choose to drive up to and across the Bear Mountain Bridge, that’s a winding, mountainside type drive. Once across the bridge, you’re right near Bear Mountain state park. On the way back, there are small parking areas to stop at and take pictures of the Hudson River and Indian Point.
If you’re thinking about the Hudson Valley, I would highly recommend the Mohonk Mountain House. It is spectacular, with the lake, miles of trails and a great funky meandering main house. If you can afford it, I would stay overnight (room cost includes breakfast, lunch, tea & cookies and dinner).
We have been there in spring/summer and winter (Xmas up there is da bomb) and we have never been disappointed.
FDR’s home in Hyde Park or Cooperstown for the Baseball Hall of Fame are short trips from NYC.
I’m not sure Cooperstown qualifies as a short trip: it’s a good 4 hours each way (from the GW Bridge).