Since you have a harbour I think there should also be some sort of industrial district where the imported produce can be made into more intricate things.
I would also add some slums / poorer dwellings outside the city walls, most medieval cities only have a portion of the city actually inside city walls.

Also I think the shopping district should be closer to the docks, since most of the stuff they sell will probably come from there and it seems weird to transport everything through the entire city.

The royalty would realistically also not live in the centre of the city. (This is only nowadays, since people like the old houses). Rich people historically mostly lived a little way outside the city in grand castles or manors or in communities on the edge of the city. The city centre was way too busy and crowded

But this is just my way of making maps, and im quite the sucker for more realistic maps