Mornagest, this is looking much better, but there are still a few layout features which might need work. Feanaaro is right that streets are usually fairly straight (although not perfectly straight). I hope you don't mind, but I thought it would be easier to show you my suggestions rather than explain them, and so I've done a quick edit of your map.
This is what I was aiming for: the red and green lines represent the primary and secondary roads of the city (green are the roads unchanged from your version, red are the ones you might want to consider adding). The yellow triangle ('B') looks a bit out of place. The easiest solution would be to add it to the palace district. The other yellow area ('A') is where the port is presumably going to go. 'C' is just somewhere I think you would be likely to have a large and impressive monument or building (eg. temple, statue, senate, whatever).
Because you asked about buildings too, I've done a quick city block, showing a possible layout for the buildings in it (red boxes = buildings, blue lines = alleys). The white boxes behind the buildings are the private yards of the different buildings, a common feature in medieval cities - again, some online research will give you an idea (Amsterdam, I think, is quite good for this). It might be worthwhile deciding which streets in your city are major (primary) roads and which are minor (secondary) roads. Buildings are more likely to line up along major roads, than minor ones.
When I made this picture I was trying to keep it consistent with what you have said about the city in the past, and also to make it the least amount of extra work for you. I have made no changes to the palace district, the district in the lower left, or the suburbs outside the walls.
Now please please please do not take this image as anything but a suggestion. You are the cartographer, and you must make the decisions. What I have drawn was done very quickly and is probably inaccurate in a number of ways.