Is this Q only for things like blogs or is it also for things we can do with the existing site to increase it's public awareness?
If the latter, then I think one thing that can be done is more questions, particularly ones with surnames, places, sources. This will increase our hits by people looking for the answers to their questions and then make them more likely to ask questions of their own. Using how-should-i-distinguish-siblings-named-identicallyhow-should-i-distinguish-siblings-named-identically as an example, they might hit on the name MEDWELL. That particular question is not likely to have the answer to their question, but they find this site and then ask their question here.
A related avenue of more questions is meta question now-or-at-a-future-point-will-we-allow-a-form-of-peer-review-in-the-spirit-of. It appears people are for doing this, but not on genealogy.se and not at this point. I think it is appropriate (if you agree or disagree - let your opinions be known on that question) and I think doing it would be a kind of publicity in it's right. Those types of review questions would have more surnames, places, sources and therefore increase the traffic to the site - which is the ultimate goal of this site.
Another related answer (ie more questions would help increase hits and be a form of publicity) but it has a negative score at the moment as not the thing to focus on.
If the answer is inappropriate for this question (ie this Q is just about blogs/socieites/etc and not about self-publicity thru google hits) then I can delete this answer.