Our caracters have been to a bunch of diplomatic affairs, to religious ceremonies, and other cultural things. On shore leave episiodes, they have to go out and find stuff to do, but when they visit planets, there's usually something diplomatic going on (a new race or political power pulling up to your planet would most likely not get the 'hi, captain. why don't you come down for a little talk' thing. It's a photo-op...politicos love that.)
Any change of command on the ship is a function, we play out a lot of the promotion/award ceremonies that happen. When you get a flag rank officer on board, there's the usual scramble by the junior officers to make the place look nice (so the admiral can then poke his head into one room, say 'nice', then ignore the rest of the inspection...)
Was that the kind of stuff you were talking about?
"War is an ugly thing but not the ugliest of things; the decayed and degraded state of moral and patriotic feelings which thinks that nothing is worth war is much worse. A man who has nothing for which he is willing to fight, nothing which is more important than his own personal safety, is a miserable creature and has no chance of being free unless made and kept so by the exertions of better men than himself."
John Stuart Mill