A little-known fact about Stack Exchange is that, on the Hot Network Questions list at SE.com, in the top right corner of the page, there's a little box for "Today's Featured Site": each day, a different site on the network gets "featured" in that spot.
Yeah, it's a little-known fact. I've met people who've been prominent users and moderators for years and never knew (or maybe forgot) that that existed. But choosing (even randomly) a network site each day to promote is actually a really nice thing to do: it helps to spread visibility of the network, and while writing this answer I came to the conclusion that promotion at the site level - not the question level (like HNQ, where people see individual question titles) and not the broad topic level (like the new footer, where people see very broad topics of interest like "Science" or "Culture & recreation") - is the best way to cross-promote within the network.
Especially for sites where the existing posts are skewed towards a particular subset of the scope: the HNQ will naturally be even more skewed the same way, and it becomes a vicious circle wherein new users joining over time will have a stronger and stronger tendency to have interests in that same subset. Promoting the site as a whole might be a good way to bring in people who're interested in other parts of that topic, not necessarily the same subset that the existing community is weighted towards. And diversity of interests and topics is a good way to make pretty much any site thrive.
So, how about doing something else with the "Today's Featured Site" thing? Like sticking it somewhere more visible than a corner of a page that almost nobody ever visits, for a start. I'm leaving this discussion post very open, as I don't have a clear notion myself of how it could/should be used. Ideas, anyone?