Spray skillet with cooking spray and heat over medium-high.
Thinly slice cheese, tomato, avocado, and onion.
Place one slice of wheat bread into the hot skillet; top with cheese, tomato, avocado, onion, another slice of cheese (this will help contain the juice from the tomato and keep the bread from becoming soggy), and then a second slice of bread.
Spray the top slice of bread with cooking spray.
Cook until bread is golden and cheese has melted, flipping halfway through cooking to brown both sides. Spray skillet with more cooking spray as needed.
Slice sandwiches in half if desired and serve with grapes on the side.