Chop tomatoes, bell pepper, and onion; mince garlic. Toss together in a bowl, along with the juice of the lime, salt, pepper, and sugar. Set aside.
Heat a griddle or heavy frying pan over medium. Add one tortilla to the pan and sprinkle with 1/8 cup shredded cheese; top with another tortilla. Cook until cheese has melted and tortillas are golden brown, flipping halfway through. Repeat with remaining ingredients.
Cut quesadillas into wedges, and serve with tomato salsa and plums on the side.