In a medium pot, combine the sugar, three-quarters of the cilantro (reserve the rest for garnish) and 1/2 cup water. Bring to a simmer over medium heat. Remove from the heat and allow to cool. Strain the cilantro syrup and store in the fridge.
In a blender, combine the ice water, lime juice, cucumber, avocado and cilantro simple syrup. Puree on high until blended. Strain through a fine-mesh sieve into a pitcher. Chill until ready to serve.
Divide the mixture among tall glasses filled with ice and garnish with cilantro and lime wedges.