Harbor, haven, port are comparable because they have at one time or another meant a place where ships may ride secure from storms.
Harbor applies to a portion of a large body of water (as the sea) that is partially or almost wholly enclosed so that ships or boats may enter it for safety from storms or may be anchored or moored there in security. In extended uses harbor carries over the notion of quiet and safety inherent in its basic use.
Haven is chiefly literary or occurs in names of towns and cities where a natural harbor (as a bay, an inlet, or a river mouth) exists and where boats may go for safety during a storm. More than the other words here considered, it connotes a refuge or place of quiet in the midst of storms.
Port denotes both a place of security for ships and one suitable for landing men or goods. Consequently, in extended use, it suggests a destination or goal. In commercial use port applies to a place, sometimes a harbor, sometimes, especially in place-names, a city or town and its harbor, but still more often in the case of the great ports of transatlantic and transpacific shipping all the approaches, all the inlets, all the facilities (as docks, wharves, and offices) involved in the business of loading and unloading ships or of embarking and disembarking passengers.