I would love to have the ability to visit different buildings when not at sea. Even if it's just in a simple menu. Something like "visit tavern", "visit shipyard", "visit church", "wander around town" you click on it and a picture pops up with a randomly selected text describe what happens and let you choose between different outcomes (a la "King of the Dragon Pass" if anybody ever played this gem). Outcomes should have very small impacts for most of them, like " one crew member is hurt" or "gain 2 fresh food", but some of them could add some significant bonus or malus if the risk is well balanced, this would add some really cool littles stories to write on your captain log.
Example : My ship arrives in Cherbourg with a load of tobacco, since my crew just crossed the atlantic seas and needs some well earned rest and amusement, i decide to hit the tavern before selling my tobacco, a text and picture pops up, and tells me I'm being approached by a man claiming he will buy my tobacco 20% over the normal price. Should I accept, the outcome could be : 1) Everything goes as planned, I make a significant profit form that event (75%) 2) The trade authority hears about this, and my tobacco is confiscated (25%).
I can think of hundreds and hundreds of those little stories.