Day Hiking Part 1

Harriman State Park (New York)
http://nysparks.com/parks/145/details.aspx

Harriman State Park is about an hour from Stamford, CT.  There are several hiking trails, and you are probably best served by stopping at the visitors center to buy a trail map before beginning your hike.  The trails are marked with different colors (white, blue, red, and yellow).  Some of the trails are part of the Appalachian trail.  There are also some good views of Bear Mountain and the Hudson River.  Driving home along Route 9W you are along the Hudson most of the way.  It was pretty last weekend (early April), but it should be breathtaking when the leaves are back on the trees and particularly in the Fall.

Bear Mountain State Park (New York)
http://nysparks.com/parks/13/details.aspx

Bear Mountain is also in the Palisades region of New York and just north of Harriman.  It has additional hiking trails.  Other features at Bear Mountain include a merry-go-round with hand carved seats representing local animals, a zoo, an ice skating rink, cross country skiing, and trailside museums.  The Harriman Visitors' Center has more information. 

If you are really into hiking, New York offers the Empire Passport, which gives unlimited access for a season for $65/vehicle.  If you visit the parks before the season starts, they likely will not be collecting fees and you can park and hike for free.

Harriman and Bear Mountain are very close to West Point and several historical battlefields.