Preheat your oven to 350°F (175°C). Wrap the outside of a 9-inch springform pan tightly with heavy-duty aluminum foil to prevent water from seeping in later. In a medium bowl, combine the graham cracker crumbs, 1/4 cup sugar, and half of the chopped pistachios. Pour in the melted butter and mix until all crumbs are moistened. Press the mixture firmly and evenly into the bottom of the prepared springform pan.

Bake the crust for 8-10 minutes, until lightly golden and fragrant. Remove from oven and set aside to cool slightly while you prepare the filling. Reduce oven temperature to 325°F (160°C).

In a large mixing bowl, using an electric mixer on medium speed, beat the room temperature cream cheese until smooth and creamy, about 2-3 minutes. Gradually add 1.25 cups of granulated sugar and continue beating until light and fluffy, scraping down the sides of the bowl as needed.

Reduce mixer speed to low. Beat in the eggs one at a time, just until combined after each addition. Be careful not to overmix the eggs, as this can incorporate too much air. Stir in the room temperature sour cream, lemon zest, lime zest, lemon juice, lime juice, and vanilla extract until just blended and no lumps remain. The batter should be smooth.

Pour the cheesecake filling evenly over the partially baked crust in the springform pan. Place the foiled springform pan into a large roasting pan. Carefully pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan. Transfer the roasting pan to the preheated 325°F (160°C) oven.

Bake for 50-60 minutes, or until the edges are set but the center still has a slight jiggle. Turn off the oven, crack the oven door open slightly, and let the cheesecake cool in the water bath in the oven for 1 hour. Remove from the oven and water bath, carefully remove the foil, and let it cool completely on a wire rack at room temperature. Once cooled, refrigerate for at least 6 hours, or preferably overnight, before serving.

While the cheesecake cools, prepare the cherry topping. In a small saucepan, combine the cherries and 1/4 cup granulated sugar. Cook over medium heat, stirring occasionally, until the cherries begin to break down and release their juices, about 5-7 minutes. In a small separate bowl, whisk together the cornstarch and cold water until smooth to create a slurry. Pour the slurry into the cherry mixture, stirring constantly. Continue to cook for another 1-2 minutes, until the sauce thickens. Remove from heat and let cool completely before spooning over the cheesecake.

Once the cheesecake is fully chilled and set, carefully run a thin knife around the edge of the pan before removing the springform side. Spoon the cooled cherry topping generously over the cheesecake and sprinkle with the remaining chopped pistachios. Slice and serve cold.