If you find any broken links on topically related websites, you can immediately contact the website owner and inform him about it. Since you will do him a favor by pointing out a broken link, you can also kindly request a replacement with a link to your relevant resource. Of course, the replacement – your article – must be informative and useful for their audience.
Google’s aim is to provide the most relevant result for any given query. Their entire business model relies on them being able to do this, consistently, across hundreds of billions of searches. For that reason, they’ve invested heavily into understanding the intent of queries, i.e., the reason a person typed a specific thing into Google in the first place.
Organic results includes a wider range of websites—not just local businesses. While location may still be a factor in the organic results, it is not generally the dominant factor. The main factor is the authority of the website (or the credibility of the site), external links back to the site, the length of time the site has been live, and other considerations. This is why you will often see sites such as Yelp, Angie’s List, and Facebook show up high in search results.