If you don't have a room at the Doubletree, then I don't recommend walking from the hotel or train stations to Lyndhurst.
While hot and unpleasant now, next week is going to be even worse. The heat and humidity in this vicinity are ghastly. You will be spending a lot of your energy (and precious bodily fluids) walking around the Lyndhurst property- don't wear yourself out before then. It's a big place, with much to see and enjoy.
There are train stations at Tarrytown and Irvington, which is the stop before. Both appear close to the property and walkable, but don't let it fool you. From the Irvington station you have to walk up a steep hill for nearly a mile, then it's a mile from there down Broadway to the property. The Irvington station is technically closer, and the walk to the Tarrytown station is an epic journey of sweat and panting, which will leave you quite uncouth. There wasn't much left of my Stuart, Helen and I when we went there a few years ago. The cab from the Tarrytown station to Lyndhurst
Dress cooly, make arrangements to share a car with fellow fans, drink water often, and wear comfortable shoes. The lawn of Lyndhurst make look smooth and flat, but it's not exactly a golf-course, and is full of lumpy, irregular terrain ("curious terrain!"- :-) ) and a few roads are thick gravel. Plus there's a lovely hill to climb as well. Keep the cha-cha heels and wedges-of-death home, folks!
And for those of you who will attempt the journey on foot, once you've gotten onto the Lyndhurst estate, the nearest restrooms are directly behind the greenhouse, to the right of the property.
I shall be the tall gentlemen in the "Please don't ask me about Night of Dark Shadows" T-shirt. :-)