Bring vinegar to a boil in a small saucepan over medium-high heat. Reduce heat, and simmer until vinegar is reduced to 2 tablespoons (about 2 minutes). Remove from heat; stir in honey. Cool to room temperature.
Prepare grill to high heat.
Place peach wedges on grill rack coated with cooking spray; grill 30 seconds on each side or until grill marks appear but peaches are still firm. Remove from grill; set aside.
Combine oil and sea salt in a large bowl, stirring with a whisk. Add arugula, tossing gently to coat. Arrange arugula mixture on a platter. Top with peach wedges. Drizzle with balsamic syrup; sprinkle with goat cheese.