In blender, place ice cream, sliced strawberries, milk, strawberry syrup, vanilla and chopped cheesecake. Cover; blend on medium speed about 1 minute until smooth. (Blender will be full; blend in 2 batches, if necessary.)
Pour into 4 tall glasses. Top each shake with whipped cream topping; sprinkle with cracker crumbs. Garnish with whole strawberries.