There are New York State and many other Parks in the area.
For a short walk try the Mill Creek Boardwalk at Lewis A. Swyer Preserve on Route 9J north of Stuyvesant, NY.
Claremont was the home of Robert Livingston. The King of England gave him a grant that covered all the land he could see from this spot.
There is a impressive waterfalls on the Kinderhook Creek at Stuyvesant Falls just east of Route 9 and North of Hudson, NY.
If you love to go “birding” try the Wilson M. Powell Wildlife Sanctuary in Old Chatham. Their website also has other spots listed.