Hey,
So in my experience most "local" sites often dont have a very high authority. The ones that do are usually your local news outlets or established local blogs. IE: Torontolife.com or Narcity (across Canada). Topical link building will absolutely help improve authority and should be done to help build brand presence however you are correct it wont exactly build you local relevant backlinks.
Id focus on a local backlink strategy. Start first with the the obvious like local chambers and business directories that allow website links, then Id start looking at local organizations that are looking for local businesses to sponsor or support them as that will help build local referring domains (These domains are usually not very high in authority but are strong local domains). You could also look into sponsored content, earned media or even ego baiting with super topical/relevant content to some of those larger news/blog outlets that are both local and authoriative because they are considered media publications.
I hope this helps!