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Are you asking about local/Maps rankings or organic?
For local/Maps, distance is a heavily weighted ranking factor. A business ranks best right around its location, and then the Maps ranking declines the farther the searcher is from the location. So, if you want to rank in Maps across a large area, you want to make sure the searcher is always close to your business. Solutions: open multiple locations! However, this really only works for coffee chains, ATMs, pharmacies, etc. It's not a practical solution for, say, a law office.
For organic, in some cities, it may be effective to create a service area page for each neighbourhood. However, this would only be effective in cities where people talk and search in terms of neighbourhoods. E.g. If Van Nuys residents search for "Van Nuys plumber", for example, then a Van Nuys neighbourhood page could rank well. Of course, not all cities have such a strong sense of neighbourhood.
Look at long tail keywords. If you create content focused on very specific services, it is less likely that other businesses will be targeting those same keywords. You can rank for those keywords over a much larger area, both in local and organic.