In a small saucepan, bring the balsamic vinegar to a boil over medium heat. Reduce heat to low 7 simmer, about 10 minutes, until reduced to a syrup consistency. Set aside & allow the balsamic glaze to cool.
In a medium bowl, combine the baby arugula & red onion. Pour the white balsamic vinegar & extra-virgin olive oil over the arugula mix & toss gently until coated well. Season with salt & pepper. Arrange watermelon chunks & goat cheese on top of dressed arugula & drizzle with balsamic glaze. Serve immediately.