Although Haiti was originally settled by the Arawak and Taino tribes ( http://www.tripadvisor.com/Travel-g14... ), the area which is now Port-au-Prince was never permanently settled by Native American tribal cultures.  It is believed that this is because its coastal location made it an easy target for attack.  Indeed, when Spanish explorers reached Haiti (beginning with Christopher Columbus at the end of the fifteenth century), it was Port-au-Prince they first conquered and took over as their own.

When the Spanish took control of the island, the tribal leaders (first Bohechio and then later his sister Anacaona) visited the area to try to co-exist with the Spaniards.  At the beginning of the sixteenth century, the majority of the tribal leaders were murdered in a sneaky attack when Spanish leaders invited them to a feast, got them drunk and then coldly executed them. 

The Spanish did not rule in the area for long before the French moved in and took over.   After they had gained control there, the French used it primarily as a base for further world exploration.   Port-au-Prince remained undeveloped for a long period of time.   It was not until the middle of the eighteenth century that the area was developed and it was not until 1770 that Port-au-Prince became the capital city of the area.