Heat grill. Drizzle both sides of tuna steaks with oil; rub with garlic. Let stand at room temperature for 15 minutes to marinate.
Meanwhile, arrange tomato slices around outside edge of large serving plate or platter. Arrange cheese slices inside ring of tomatoes, overlapping tomatoes slightly. Drizzle with vinaigrette; sprinkle with basil. Set aside.
When ready to grill, place tuna on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 8 to 10 minutes or until fish flakes easily with fork. Do not turn tuna. Flake fish into chunks; arrange in center of tomatoes and cheese on platter.