Preheat a gas or charcoal grill on medium high heat.
Toss all the vegetables with olive oil, salt and pepper. Thread the onions and tomatoes onto separate pre-soaked wood or metal skewers. Arrange the vegetables on the grill grates. Grill, turning occasionally, until the vegetables are tender and lightly browned, 8-10 minutes for onions, 5-7 minutes for peppers, squash, zucchini and eggplant and 2-4 minutes for tomatoes.
To make the sandwiches, spread the cut sides of focaccia with pesto. Arrange the goat cheese on the bottom sides of the focaccia and top with arugula and the remaining focaccia.