Talroth, you are off to an excellent start. The layout is interesting and varied, and I'm curious to see how this map develops. I like the spiderweb like tracery of the smaller roads--well done.
Now, for a few brickbats First, I'd change the color of the grounds around the city from brown/tan to green. Why? Brown, black, tan, and other darker colors are typically used to depict the building and roads of cities whereas green and the lighter colors typically depict the outlying farms and fields. Its a convention to be sure, but I think using green or some other lighter color on the non built up areas would provide better contrast and a better look to the map.
Second, too many walls. Unless this is your fantasy version of Malta that is exposed to some massive seaborne threat, the number of walls can be reduced greatly. Why? In the middle ages, massive iron chains (see history section in the article, 2nd paragraph down) could be extended across rivers and the entrances to bays, preventing the passage of ships. Unless your city is threatened from both the river and the sea, it looks highly defensible, as the exterior walls and chains across the marine passages can block most entry and exit. I would keep the walls on the outer islands and the river island which are part of the perimeter defense and the kings island (security, no doubt), but tear down the inner walls that border the port areas and the walls on the south inner island. Yes, nobility and wealthy merchants live on that island, but boat patrols and guardsmen are far cheaper than the maintainance and upkeep on the walls around the island. City walls, in a sense were the medieval version of the strategic defense initiative--a very costly defense system taking years to build with significant sums of money required to upkeep. Unless your kingdom is fantastically wealthy, I don't see them maintaining any more walls than they have to.
Third, while I'd keep the wall around the castle in the west city (sort of a bastion of last resort in case the outer wall is breached), I'd knock down the walls that separate the two districts there and link the northern parts of the districts up by road (the south district near the islands looks like an add on, keep the wall up between it and the rest of the city). Given that the west city is primarily poor and working class now, I just don't see the nobility and the king spending money to maintain the interior walls (except for the one around the castle). Also, although it could take decades to occur, as cities expanded they would sometimes knock down and enclose larger areas within their walls. Given that your city has grown since it founding, I see interior walls existing within in for one of three reasons--defense/guarding a major fortification or bastion, security/keeping the riffraff out, or social control. If a wall doesn't meet one of those criteria, knock it down.
Fourth, where are the piers? I know we are looking at your city from a really high vantage point, but given the riverine and maritime commerce present in the city, it is likely to be very busy and have a lot of port facilities (think New York, New Orleans, Hamburg or Shanghai). There should be quite a few piers and areas to tie up boats present. Also, I would "thin" out the spiderweb road grid in some parts near the water where you want port activity (ie near the piers)--because instead of the usual residential or commercial blocks, you would have warehouses, seinyards, shipbuilding facilities as well as fish salting and processing facilities that take up quite a bit of space.
Fifth, what are those hexagonally shaped buildings near some of the circular street junctions--mini keeps? Towers?
Sixth, while I assume the circular street junctions can function as market areas, it would be realistic to have an "extra large" circular or square area on each side of the city functioning as a market. In fact, given the size of your city, I would not be surprised to see 3 or 4 markets service different areas of the city.
Lastly, where are the bridges? Given a city the size of yours--if its a half mile to the half inch--you're talking about a built up area of several square miles and a city population of 50k-100k+ (which was huge for the middle ages--think Mexico City, Tokyo, Shanghai, New York, or Mumbai in modern terms). That size city would be able to afford bridges. For instance, since the outer rim islands are inhabited, I suspect that many of them would have bridges linking them with the mainland. Bridging the half mile between the eastern and western parts of the city might be at the very limits of medieval building technology (unless caissons or artificial islands were built) and I suspect the king would not want to have bridges to the riverine island unless the city walls had expanded to protect either bank, but the distance to the smaller islands would be bridgeable within the constraints of medieval technology. Of course a kingdom with access to wizardry (I have no idea if your campaign is high or low magic) would be able to do much more.
Take my advice with a grain of salt Talroth. I usually approach map commentary from a point of realism and what I've seen done historically. Given that this is a fantasy city in a fantasy world, do what you like.