Well, you could something if the city burned to the ground…

I don’t know if a strict grid would be a good idea, though. You’ve got those three hills that make grids difficult, and the main diagonal avenues have important purposes, so I wouldn’t want to get rid of them:

If I was redesigning the city, I’d focus more on a spoke-and-hub model. The unnamed square near the Great Sept should be moved and/or expanded a bit to the east where the exact center of the city is, so that it connects directly with the Muddy Way and is more in line with the rest of the gates. Moreover, the city at present lacks a main central plaza for public events and that location would do nicely.

Next, the King’s Gate, the Lion Gate, and the Old Gate lack a major avenue connecting them with the heart of the city, which is bad planning since each connects with a major road and you want traffic to move more smoothly. So I would extend the Muddy Way up to the Old Gate, connect the Rosby Road to the Gold Road, build a new road from the King’s Gate up to that central square past the Great Sept, and extend the Street of SIsters past the Dragonpit to the Dragon Gate. (Honestly, I’m shocked that the East Barracks of the City Watch isn’t directly connected to any major thoroughfares – how do they expect to respond to any crises over int he west of the city? And why isn’t there a Central Barracks?)