Scoop flesh from watermelon half and transfer watermelon to a blender. Add 2 cups cold water. Place a folded towel on blender lid and blend until liquefied, about 1 minute. Strain through a fine mesh strainer into a large bowl to remove fibers. Discard fibers left in strainer. Skim and discard excess foam from juice if desired.

Place sugar and 1/2 cup water into a saucepan over medium heat and stir until water is hot and sugar has dissolved. Turn off heat and let simple syrup cool to room temperature. Stir simple syrup into watermelon juice to taste.

Pour drink into a 2-quart pitcher and refrigerate until cold, at least 30 minutes. To serve, fill tall glasses with ice cubes and pour agua fresca drink over ice. Serve with straws.