Why this is not just SEO with a city name added
Ordinary SEO ranks pages. Local SEO ranks a business listing, and Google scores that listing on three things — how close you are to the searcher, how relevant your categories are, and how well known you are. Only two of those are things anyone can work on, which is why local SEO is mostly profile, category and review work rather than page work. A site can rank nationally and still be invisible in the map pack three kilometres away, and the fix is usually nothing to do with the website.