Been there many times. You take the Long Island railroad from Manhattan right to the track. About 40 minutes maybe. If the weather is nice it's a great time. Take a blanket and sit on the grass near the home turn. Warning, if there is a chance for a triple crown the crowds will be big and some years they haven't opened the betting windows. A good alternative is to reserve a table at The Winner's Circle. It is an OTB/ restaurant. It is located near Madison Square Garden. 7th Ave in the 30s.