You can drop them right in the heart of 'enemy' space almost without challenge.  Playing against a Human such an act would probably start a war but against the AI it gets slightly irritated at worst, and such irritation is easy to mitigate with the odd trivial gift here and there.  The AI doesn't seem to consider culture warfare as a credible threat.

Thanks for the clarification guys, but doesn't that mean you end up with a metric fuckton of culture starbases if you're pursuing an influence victory? In my last game I had them everywhere, it was a nightmare keeping up with all of the constructors.

I've got a follow up question. Does the effect of influence diminish based on distance? Let's say I have a planet that's generating a huge amount of influence, due to buildings and natural tile yields. However this colony is right at the heart of my huge culture borders, is it accomplishing anything?

You can hover your mouse over the map where cultural influence is present and see how much of yours / theirs is in place.  Everything radiates out from sources, slowly growing weaker as it has to overcome places where there is no / enemy culture.