Besides making money (mostly through ad space sales), Google has 2 main jobs:
1. To produce the most relevant search results.
2. Influence popular opinion by elevating some information, while suppressing other information.
We won't be tackling the second part in this article, but we will discuss the first.
When you engage in SEO for your city (and in big markets, your neighborhood), it's not wise to expand your keywords beyond your physical city. This is because you're taking away keyword opportunities that would feed your main search terms, in the hopes of ranking in a neighborhood or city you aren't physically located in.
Unless you're in a very low-competition market, Google will not even consider showing your site for organic rankings in a neighborhood, city, or zip that it doesn't see you physically located within.
It's best to keep a focused SEO strategy and then utilize Google ads to saturate neighboring towns and communities.