I tried exactly the same project when I was working in Birmingham many years ago, working with one of the A-Z street maps. Started with A Street, which was in a far-flung industrial area. I didn't get very far through, but this seems like an adventure...
I tried this too a few years ago in my suburban local council area (the City of Banyule) in Melbourne, but I'd bitten off more than I could chew (it's 63 square kilometres) and only got towards the end of the As before moving out of the area a year or so later.
Wow that is a lot of ground to cover! Salem is a bit more manageable for sure. I think I will just use city strides to complete streets alphabetically, so some will get completed along the way. Let’s see how far I get! Back to the same part of town next week, didn’t quite have enough time to fit in all three streets on this one!
I did nine runs of my local burbs AtoZ in the first two months of lockdown, then have only done one since mid June, so hopefully your motivation lasts longer than mine! (Though we have been able to go further afield to run since then so have been taking advantage).
I'm only approaching the end of the Ds, so could take a while...
In our area the streets are alphabetical north to south. If I got dropped off at the top I could run the alphabet!