Combine zucchini, squash, onion, and bell pepper in a large bowl. Drizzle with 1 tablespoon olive oil, and toss to coat.
Grill, uncovered, over medium-high heat (350º to 400º) for 10 to 12 minutes, turning once, or until just tender.
Whisk together vinegar, salt, and pepper in a large bowl; slowly whisk in remaining 2 tablespoons olive oil. Add grilled vegetables and basil; toss to coat. Sprinkle with goat cheese just before serving.