Mix the graham cracker crumbs, sugar, melted butter, and chopped pistachios. Press into the bottom of a 9-inch springform pan and refrigerate.
Beat softened cream cheese until smooth, then add powdered sugar, vanilla, lemon zest, lime zest, lemon juice, lime juice, and sour cream. Mix until smooth.
Whip heavy cream to stiff peaks, then gently fold it into the cream cheese mixture.
Pour the cheesecake filling over the crust and refrigerate for at least 4 hours or overnight to set.
For the cherry topping, cook fresh cherries with sugar and lemon juice over medium heat until they release their juices. Add cornstarch if desired and cook until thickened.
Let the topping cool, then spoon over the chilled cheesecake.
Garnish with crushed pistachios and fresh cherries before serving.