Preheat the oven to 325°F.
In a bowl, mix together the graham cracker crumbs, 1/4 cup sugar, and melted butter. Press the mixture into the bottom of a 9-inch springform pan.
In a separate bowl, mix together the cream cheese, 1 cup sugar, and vanilla extract until smooth. Beat in the eggs one at a time.
In a small saucepan, mix together the blueberries, 1/4 cup sugar, and cornstarch. Cook over medium heat until the mixture thickens.
Pour the cream cheese mixture over the crust in the pan. Drop spoonfuls of the blueberry mixture over the top of the cream cheese mixture. Use a knife to swirl the blueberry mixture into the cream cheese mixture.
Bake the cheesecake for 60-70 minutes, or until the center is almost set. Allow the cheesecake to cool before removing it from the pan and serving.