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.