You've definitely captured that look of the city having expanded over time, that's probably the most compelling feature of the layout. Having a story in your head of how a city has grown over time and showing that on the page is a great way to make a city feel real and grounded.

Looking back at this post I was having a bit more of a think about it and realised that the most logical place for the docks is actually up the river bank through the oldest sections of the city as the docks would have been built at the same time as these sections. In a medieval-like fantasy world, the only way a city would grow to this size would be if it was a trade hub and at this time (and still today actually) ships are the most efficient way to transport large volumes of goods. If the first bridge was removed and the river widened a bit up to the point where the second bridge is, docks could be put along the sides. the city could either have very high bridges to allow large ships to navigate upriver or the docks could be a point where goods are transferred to and from riverboats to allow movement up the river.