No, Trinidad does not have any significant peninsulas. The island's coastline is relatively compact and irregular, but lacks the distinct, narrow land projections (peninsulas) that characterize places like Florida, Baja California, or the Yucatán.
Tobago (30 km NE) is the "sister island"—not a peninsula. Smaller islands: Chacachacare, Huevos, Gaspar Grande, Monos, Little Tobago, St. Giles—all separate landmasses.
No peninsulas means no dramatic "hook" geography driving localized microclimates or isolated communities. Settlement and infrastructure follow the east-west Northern Range and the west coast urban corridor (Port of Spain → San Fernando).