Looking good so far. I like that you've done it in city blocks rather than individual buildings - it's much more realistic to history, and I think it makes it more original as well. Also, I'm fascinated to know the story behind the long straight avenue that suddenly stops in the lower left.
A few comments for you. I might be a novice mapmaker, but I've studied urban planning and urban history for almost a decade, so I'll use that instead.
First, the shape of your island suggests a rugged coastline; if that is the case, you would probably need to pull back the edge of your city around the coast, as it should be rocky cliffs rather than city blocks. You would probably also have to give up on having canals (sorry 'bout that), and it might affect your right-angle roads too, but not as much, especially further inland. That's if you're sticking to familiar geography, anyway.
Second, it seems obvious, but city wall? Unless you have a specific reason for not including one (magical protection, perhaps?) the city wall would often leave a strong mark on the city - there would usually be a road around its inner circumference and again around the outer, so that when the wall is gone, it leaves two parallel roads making a circuit of the city as it existed then. Again, I don't know if you chose to do this deliberately, but the very abrupt and very straight transition from old to new town would probably also be less vertical if you had an old city wall.
Third, where is the point of origin for this city? I saw you mentioned witches and magicians, but on a more mundane level what about the harbour? If this were a real-world city, the harbour would probably be the focus of the old town, with lots of roads radiating from it. Alternatively, that peninsula in the upper right could be a fortified position (which the current configuration could still be), which would mean the streets outside the fortress would be more like the old town, and the new town would be elsewhere.
Last (don't want to bore you too much), although a lot of old cities had continuous street facades the entire length of a building block (which you've done), they often had large internal courtyards. If you look at, for instance, St. Petersburg in Russia, many building blocks had lots of courtyards, some that look too small to be useful, and others large, all over the place, and with no apparent access from the street.
Since you've made this map in city blocks, and it already looks like a convincing old-style city, I think you have a real opportunity to go down that historic route. Just a couple of thoughts, anyway.
Look forward to seeing where you take it.