Rather than doing any specific "thing" to increase rank, it's better to understand why those places help you grind rank, so you can find your own places to do it.
Use the Galmap to look for systems in states such as famine, outbreak, conflict or war and consider how far they are from Sol, what their population is, whether there are other systems nearby and how many factions are present.
Any system in one of those states, with a couple of nearby systems that have similar factions, will be ripe for allowing you to increase rank pretty easily.
Was talking to somebody, last night, about this while in Merope.
Had a quick look and thought a system called Bhumbla (sp?) would be a good candidate for Fed' ranking.
Arrived and it's full of donation missions, data-delivery missions to nearby systems and a variety of assassination/massacre missions for when you get bored.
It's probably not quite as prolific as some of the "famous" places but it's certainly viable for rank-grinding, especially if you're willing to mode-flip.
I'm not saying "Go to Bhumbla for Fed' ranking!!!"
I'm just pointing out that it's pretty easy to find suitable places if you know how to look for them.
Also, mining missions to gain rank?
No thanks! [where is it]