Spread goat cheese on tortillas. Divide mango, onion, jalapeno, and cilantro on one half of each tortilla. Fold tortilla over filling.
Heat a large heavy skillet over medium-high. Working in batches, cook quesadillas until cheese softens and tortillas are crisp and browned in spots, 1 to 2 minutes per side (if skillet begins to scorch, reduce heat to medium). Transfer quesadillas to a cutting board and cut each into 4 wedges. Serve immediately.