There's an interesting map on the City Council website that shows the gritting routes and where the grit bins are.
You can look up your own address, or you can move the map around from north to south, east to west to get a sense of the bigger picture.
The link to the map is here.
Interestingly, there are several roads I spotted that don't get gritted and yet are on bus routes or right by day centres with mini buses coming in and out. Makes you wonder what is a priority area and what isn't!