For the most part, using structured data for organic SEO is about getting some rich snippets into the search results. For local SEO however it can have a strong impact on your local rankings.
Local rankings are probably the most volatile there are. That doesn’t mean they’ll change every few minutes but that a search for the same keyword will produce a lot of different results based on the searcher’s location. If the search engines can determine that your locality is relevant to the searcher’s location, then you’ve got a better chance of ranking.
Properly implemented structured data can give the search engines the information they need to determine just that. Whether they are reading your physical address, phone number, or even local reviews, all of this can play a role.
If you haven’t gotten around to implementing structured data for the rich snippet value it might bring to your organic results, you should do it for the local value.