In medium nonmetal bowl or resealable food storage plastic bag, mix sugar, salt, garlic, vinegar, oil and mustard. Add cheese, tomatoes and olives. Cover and refrigerate at least 2 hours to marinate.
With slotted spoon or tongs, remove cheese, tomatoes and olives from marinade. On each of 20 decorative toothpicks or bamboo skewers, alternate cheese, tomatoes, olives and basil. Serve immediately or refrigerate until serving time.