Scope
Once you've taken a look at your Affinity Categories and found new opportunities, the next step organizations and evaluate your possibilities. If you go to their website and find that they don't link to anyone, that's good news!
If you've ever worked with a law firm, you'll be familiar with link building through scholarships. Universities across the country create listings of external scholarships on their websites, so this is a great opportunity to acquire strong .edu PageRank links.
Many agencies have taken notice and have started offering scholarships to get these links. What used to be a dozen external links on universities' external scholarship pages has turned into hundreds, diluting the benefit of the links.
What I'm trying to say is that even if (using the first idea) the animal shelter doesn't have any external links, it doesn't mean they won't consider it. Contact them and suggest it. More often than not, they are willing to do it.
Pro tip: Don't try this with the American Red Cross. We've thought of japan mobile database it before, we've tried it, and it doesn't work.
Start building your community (and local links)
If you work with a local organization that doesn't usually link and you get the link, you will have the only external link on the site!
While there may be other external links, you will likely be the only one for your industry and location.
If you start building a relationship with other organizations in your community and increase brand recognition among their members, you will gain more attention online (and in person!).