One of our recent projects on FromThePage is the Yaquina Lighthouse Collection of documents from the National Archive. I helped the team at Yaquina brainstorm ways to publicize their project and wanted to share that process here as well. This was in addition to their existing Facebook, Twitter, and Instagram publicity.
I would contact the people/groups you find below with the project link and a short bit of text that explains what you are trying to do. (Make it easy on them -- write their post/email/etc for them!) I would tailor it to each group based on their interest.
1) location or family name genealogy
-- rootsweb "surname lists": http://rsl.rootsweb.ancestry.com/
-- search on facebook for surname + "family association" "Graves Family Association"
-- search for Statename + Genweb, i.e. "Oregon GenWeb". http://www.rootsweb.ancestry.com/~orgenweb/
2) Lighthouse Interest Groups on Facebook:
https://www.facebook.com/Lighthouses-43343592942/
https://www.facebook.com/uslighthousescom/
https://www.facebook.com/Lighthouses-of-North-America-426590840685801/
3) Of course, your local history groups and local library -- perhaps the library would let you post your flyer? Or would one of them be interested in a presentation on the materials, the project, what you've found so far?
4) Websites: http://www.lighthousefriends.com/ (has an email at the bottom)
When you find a good match in Google, you can right click on the URL (www.lighthousefriends.com in this example) and Google gives you a "similar" option.
Doing this gave me the following search results, which has a lot of potential matches for you. If they have a "news" section or a blog, they likely are willing to post about your project. Once you find a good match, look for a "contact" link (usually at the bottom of the page) or a facebook page you can message them via (look for the "message" button) or a twitter account (tweet at them by using their twitter id, like: "@uslhs we thought you might like our new project <link>").