There are oodles of options. I totally second TDNY's options, especially Mianus (wonderful walk, very easy for kids). Other great options:
Turkey Mountain Nature Preserve in Yorktown Heights--easy walk up to the top (kid-able) with great vistas over the reservoir and to the Hudson.
Kitchawan Preserve also in Yorktown--lovely trails through woods and fields.
Blue Mountain Reservation in Cortlandt has great trails, some easy and some hard (up to the top with great views).
Hudson River Walk in Croton is paved and runs along the river.
John Hand Reservation in Yorktown also has great trails, but a little more challenging (not for younger kids)
On Route 6 just north of Peekskill you can park along the road and access the Anthony's Nose trail--from there it is a relatively short and not too hard walk to some amazing viewing spots.
Good resources are the Yorktown Land Trust's Yorktown Walk Book, which has maps to all the trails and reservations in town (
http://www.townlink.com/community_we...blications.htm) Also, Walkable Westchester has great info county-wide:
http://www.nynjtc.org/panel/walkable-westchester