I can never resist commenting on a city map, especially when layout is concerned.

I don't think there's any contradiction in what you're looking at (river + outer settlements).

Example: London in the seventeenth century. The city had an old wall that was no longer really needed for defence (a long period of peace had taken place), and a ditch/moat encircling the wall. The ditch was man-made, and fed by the Thames. There were also many suburbs around the city (the technical name for settlements outside the walls of a city, that still serve as part of the city). What happened is, as the defensive purpose of the walls declined, less effort was made to maintain them, and similarly, the ditch was neglected. People lived on the other side of the ditch, not right up against the wall. They would often use the land in the ditch (the neglected state also meant that it started to fill up, and dry out) as a garbage dump, and also for allotment-style gardens. It was also useful in other ways (for drying wool--London's main export--and for ropemakers, who need a long stretch of open ground). Of course, it is a different story if your moat is a running river, but it shouldn't stop your city from having suburbs.

Also, it may be worth noting how walls decay. It is relatively rare for a city to knock down old walls--that costs money and doesn't really have any advantages. Instead what often happens is people simply take rocks and bricks away for their own construction purposes, slowly causing the wall to collapse, and in the place where it used to stand, new houses get put up (there is very often a road that runs the length of the wall inside, and another outside the wall/ditch--many cities have these two parallel roads to this day).

As for a smaller wall around the old city, it isn't completely unrealistic, but it is unlikely. Small settlements don't need walls--if they are threatened, the townsfolk can gather inside a fortified citadel/castle, and their houses are left to the mercy of the enemy. When a settlement gets too big to make that practical, then a wall is constructed. A second layer of walls, then, would only occur if the city has grown significantly beyond that first level. Looking at your map at the moment, and judging scale from the features included, it doesn't look big enough to warrant two sets of walls (at least, not according to historic urban patterns--your world, your rules).

Looking good, so far.

THW