Combine first 3 ingredients in a mixing bowl; mix well. Press into bottom and halfway up sides of a 9-inch Springform pan; set aside.
Beat cream cheese at medium speed of an electric mixer until light and fluffy. Gradually add 1/2 cup sugar and flour, beating well. Add eggs, one at a time, beating well after each addition. Stir in pineapple and 1 teaspoon vanilla. Pour into prepared pan. Bake at 375° for 20 minutes. Remove from oven; cool 15 minutes.
Combine sour cream, 3 tablespoons sugar, and remaining vanilla, mixing well; spread over cheesecake. Bake at 425° for 10 minutes. Remove from oven, and let cool 30 minutes. Remove sides from springform pan. Cool completely. Cover cheesecake loosely, and refrigerate overnight.