I've taken the train to Saratoga and I've rented a car from NYC- I'd recommend renting a car. It's a nice train trip except that we were an hour late because there was rocks or something like that on the track (I don't remember why the delay). There is a bus that takes you from the station to the track and back again, and I think general admission is included in the cost (it was when I went). But the car gives you more freedom in departure time and I think is a shorter trip.
The train is a lot cheaper, because car rentals are ridonkulously expensive in the city- if you have a AAA membership, rent a car via their website; it's a bit cheaper that way (unless you've got a great corporate rate through your job or something).
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