I'm not sure who takes responsibility for promoting Stack Exchange, but it would help a lot if they could organise shout-outs on well known LEGO fansites.
A well worded e-mail sent to the site's administrators could be just the thing we need to find potential target users.
Promoting of the site is a community responsibility - each user should do it as much as he can to the persons he knows.
That said, I'm personnaly holding off a little on publicity, for the following reasons:
I tried once to communicate something to Huw Millington (Brickset) about a way to scan minifig barcodes for Android (before you could find dozens of apps to do it), and while he did respond to a few mails, I had the clear impression I wasn't really reaching to him - presumably because he's got way too much junk to sort out. I'm not saying I won't try to push bricks.se to him too, but I still feel now is not the time.
However, if you happen to stumble upon a discussion on a topic which has been asked here... it's worth sharing a link. (I've seen someone on Facebook who had just noticed the stud in minifig heads had changed, for example)
Don't forget your local LUG and/or ambassadors, too. I'll probably post something to FreeLUG someday, and through Didier Enjary that should go further to RailBricks. But as you say, it needs to be well-worded, so I'm not rushing myself there either.
