Lyndhurst Mansion is around a 45 minutes train ride on Metro-North from Grand Central Station.  Off-peak roundtrip train tickets will cost around $21.  A quick taxi ride from the Tarrytown train station to the mansion entrance is $7.  A one hour small group guided tour of the mansion is $18.  While this day trip upstate will cost you around $50, I would recommend it for the architectural and New York history as well as just walking around the grounds and taking pictures.  

Lyndhurst Mansion had 3 private family owners in its history before being turned over to the National Trust for Historic Preservation. The mansion, which sites on 67 acres of land overlooking the Hudson River has a National Historic Landmark designation.  

There are a number of tours individuals can sign-up for.  Be sure to book online in advance since you must be on a tour to enter the property.  Visiting just the grounds does not require any ticket. 

Lyndhurst Mansion is also available for private events such as weddings and once you see the estate you will see why.  The main house sits on top of a hill, there is a rose garden, a variety of trees and large lawns and because we are at a former New York elite estate, their own private bowling alley.

I would recommend visiting Lyndhurst for a couple hours before heading back into the city.