I don't believe that ports should be buildable only in higher level cities. Small towns in real life have ports too, actually cities are built and grow around ports not the other way around.
By building an outpost next to a beach a town should manage to benefit from a tech tree specialized in that area.
A port shouldn't only allow to build one kind of boat, but different ones with different speeds and armaments. Ports also should allow to have a food growt based on fish (a fishing boat fleet should be a tech to develop, small fishing boats should appear around a port with such tech.
Also a fish market could improve the income in cities that specialize in a culture based around the port.
Low level cities could allow the production of small boats good for exploration
A slightly larger city should allow to get a faster boat, that allow to carry one unit (useful to build outposts across the sea after having explored with the level one boat).
A third level city should allow to produce ships large enough to carry an army and even larger cities could produce warships and faster carriers.
I believe a tech tree could be studied to specialize cities around that kind of culture.
Maybe a higher level tech could allow to uncover parts of the world map...
Notice that the AI should learn how to use boats efficiently to cross the sea and attack enemies. That is the only way we will ever see islands in this game.
Other ideas welcome