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It's likely not to be possible!

https://en.wikipedia.org/wiki/Eulerian_path

I was going to argue that if every street had a sidewalk on both sides, then we could indeed construct an Eulerian path over sidewalks, but probably there are some streets without sidewalks on both sides.

I was thinking it was common for alleys to have no sidewalks at all, but I looked at quite a few with Google Street View, and many do have sidewalks after all (even on both sides!).

An example that I found which seems to have a sidewalk on only one side is Orange Alley, but it's complicated: sometimes the single sidewalk disappears entirely, and in tiny patches a sidewalk shows up on the other side. But I think the alleys probably will undermine your clever suggestion.

Not possible. There are > 2 intersections with an odd number of streets. (Note that this includes dead-end streets)

Eulerian path through SF? Sounds like a hard problem. :)

You may be thinking of Hamiltonian paths ;)