Lightly grease a 9-inch springform pan. Combine the graham cracker crumbs, 3 tablespoons white sugar, and butter in a bowl and mix until evenly moistened; press into the bottom of the prepared pan.
Cream together the cream cheese and 1 cup sugar using an electric mixer. Add the flour and beat until smooth. Mix in the eggs with the mixer switched to low. Pour in the eggnog and vanilla; continue beating until just blended. Stop the mixer and scrape the bottom of the bowl occasionally. Pour the mixture over the crust.
Fill a shallow dish with some hot water and place on bottom rack of the oven. Put cheesecake on the middle rack of the oven. Turn oven heat to 200 degrees F (95 degrees C). Do not preheat oven.
Bake the cheesecake until the center is set, about 3 hours 15 minutes. Turn oven off. Allow cheesecake to cool in the oven, about 3 hours. Chill in refrigerator overnight.