A couple of days ago I was showing Politics to a friend, hoping to get her to participate on the site. At some point, she noticed the "hot questions" list and I couldn't help but notice that until she read the 5th or 6th question on it, she wasn't impressed. Now, don't get me wrong, those first few questions were excellent. However, they were on topics that didn't really interest her (programming, physics and gaming, if memory serves). There even was one question that looked like complete garbage to her (a Unix & Linux question, with some bash command in its title).
A few minutes later we had moved on to stackexchange.com, and were browsing the sites list. When she noticed that we have sites on related subject matters (namely History, Philosophy and Skeptics), she asked me why there weren't any questions from those sites in the "hot questions" list. And I think she has a point. As a programmer, I find at least a couple of interesting questions on the list every day. However, I don't think the list works equally good for someone who isn't that interested in programming, or IT in general.
What I propose is simple: We should heavily promote questions from sites related to the site a visitor is browsing in the "hot" list. When I'm at The Workplace, I think it'd make sense if questions from Freelancing would get a bonus and appear a bit higher than questions from - for example - Programming Puzzles & Code Golf. When I'm on Astronomy, questions from Space Exploration and Physics should take precedence over questions from Blender, etc.
I'll admit that - other than the obvious - I don't have a decent suggestion on how to group the sites. I have absolutely no idea what people browsing Anime & Manga would be more interested in seeing from the rest of the network. Perhaps, if this or something like this goes through, it would make sense to ask each community what sites they feel are more closely related to their own subject matter.