Crust: Stir together graham cracker crumbs, melted butter, and 1/4 cup sugar in a medium bowl. Press into the bottom of a 9-inch spring-form pan. Refrigerate the crust while making the filling.
Filling: Combine the cream cheese, 2/3 cup sugar, salt, beaten eggs and 1/2 teaspoon vanilla in a medium bowl. Beat at medium speed for 5 minutes. Pour the filling into the spring-form pan over the graham cracker crumb crust. Bake at 350° for 25 minutes. Cool 30 minutes before adding the sour cream topping
Topping: Mix the sour cream, 3 tablespoons sugar, and 1 teaspoon vanilla together in a small bowl. Pour and spread on top of the slightly cooled cheesecake. Bake for 10 more minutes at 350°. Cool to room temperature and then place in refrigerator to chill before serving.