What is the name of the port city founded by the Spanish in 1519 in the New World?

The port city founded by the Spanish in 1519 in the New World is Havana. Havana, known in Spanish as La Habana, became one of the most important ports for Spanish trade and military operations in the Americas due to its strategic location on the north coast of Cuba. The establishment of Havana was critical to Spain's colonial empire, as it allowed for the control of maritime routes in the Caribbean, facilitating trade and the movement of goods.

The other cities listed, although historically significant, were established at different times. For instance, Cartagena was founded shortly after Havana in 1533 and became a key port as well, while San Juan, established in 1521, is the capital of Puerto Rico. Lima, founded in 1535, became the capital of the Viceroyalty of Peru and was vital for the Spanish presence in South America. Therefore, Havana stands out as the correct answer because of its founding date in 1519 and its significance in the context of Spanish colonial endeavors in the New World.