Rockefeller State Park is actually fairly easy to get to using Metro North, but for it to be worthwhile plan on a 15-20 miler as opposed to a 10.
You can take the hudson line to the Tarrytown, NY stop, a 38 min train ride from Grand Central Terminal. Then, run up the hill, east, about 1 mile, to North Broadway, which is the main drag through Tarrytown (and same Broadway that’s in Manhattan & the Bronx). MetroNorth Schedule
Head north on Broadway until you get to an intersection of Broadway (Rte 9) and 448. On the SE corner of this intersection is the Horseman Diner (a good place to eat after your run). Head east on Rte 448. In about 150 meters you will come to an entrace to a parking lot on your right. This is the Sleepy Hollow HS parking lot.
On your left, across Rte. 448, is a dirt trail, about 40 feet wide, called the Old Croton Aqueduct. You can run north on the “OCA” about 2 miles and enter the trail system for the Rockefellers.
You can print a map of the area from mapquest using zip 10591 as a reference point. Tarrytown Map
I would encourage all novice visitors to the Park to carry a map of the trail system for it can be very confusing. You can obtain a map here: