Link building is a big part of search engine marketing, and as such, there are always questions surrounding the best kind of links. Most would say that highly relevant links from authority sites are the cream of the crop. But when those links are hard to achieve, there are other types of links you could try to get.
.edu and .gov links
In the recent Google Webmaster Chat transcript, there's a snippet about .govs and .edus. Matt Cutts says that there's no PageRank boost from having such links, and it'd be especially unhelpful for you if you get a link from an .edu page that doesn't have any inbound links to it.
So why do people like .gov and .edu links? As martinibuster says, they tend to be in good neighborhoods (versus other sites, for example).
What if your site -- let's call it Site A -- has a link to Site B. Site B links to Site C and Site C links back to Site A. In other words, you're interlinking your many sites (at least in this example). Will this help you in raising search rank?
Depending on the existence of other backlinks (more are preferable), it may help. Therefore, you should aim to get a lot of links from as many properties as you can and not just focus on your three sites. Having these links can also raise (cough) your PR.