You've made a good start rwaluchow, I'd be curious to see what this looks like when fully illustrated.

I agree with the Cartographist that the road grid is too orderly and neatly laid out. I'd also "scrunch" up many of the buildings in the regular parts of town (excluding the wealthy areas) and increase the building density--space inside medieval city walls was at a premium and people built wherever they could (including up and over existing streets--in some parts of medieval Paris and London the crowding was so bad that laws had to be passed banning "overbuilding" on streets beyond a certain point since some streets stayed dark in daylight due to the overhanging structures). You even might want to think about having structures on the bridge (similar to old London Bridge).

Also take a look at some real and fantasy city maps for inspiration on how to lay out a grid--Ptolus, Freeport (especially the revised version), Waterdeep, Greyhawk, Istanbul, old maps of London and Paris, Rotterdam, and Hamburg just to name a few.