For the dressing: In a small saucepan, whisk together the balsamic vinegar and sugar. Cook over medium-high heat until reduced by half and syrupy. Set aside.
For the pizza: Slice a 3/4-inch-thick disc of watermelon from the middle of the fruit and remove the rind. Cut the disc into 6 slices (wedges), and then assemble the wedges back into a circular shape.
Sprinkle the arugula, feta, red onions and cherry tomatoes evenly over the watermelon wedges. Drizzle the dressing on top.