I am replying to this in understanding that you want to know what to do in order to rank locally - both in organic search results and in maps.
First what must be done is proper on-page.
What's important is that your website shows location relevance to the place you are trying to rank in. After usual on-page stuff, add NAP, schema, embed google map. The location page must have a lot of content about that location.
Once that's done, you should start off with some foundation links (social network profiles, video sharing links, etc - links from high DA sites), then start building maps and citations, send some social signals.
The links you ll be building should be topic and location relevant to your website. Outreach + pbn should do the work. Link out to both your website and your GMB, embed your maps in PBN or web2.0.
You can always throw in a press release as well. Of course, try that everything looks natural.
Hopefully this helped, I believe someone will surely have something to add, that I have missed.
Cheers