Schools do give positive traits to the characters who remain in that city. They also give specific ancillaries to those same characters (tutor for example). Potentially, a port of a given city could be considered part of that city, and since ships are allowed in a port (unlike neutrals/enemies) perhaps they can gain traits by remaining there for a set period of time. You would have to experiment to see though - by leaving a fleet at Athens, for example for five years and comparing that admiral to a fleet commander who had spent the time at sea.
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