Perhaps one vault could have been raided by raiders or even deathclaws (like in fallout shelter) and the surviving vault dwellers habe barricaded themself in the radio room and sent SOS signals out which your pipboy just happens to pick up when in range.
Or maybe a much calmer scenario where there's a vault overseer election and one candidate is murdered. You can either help catch the culprit and clear the other candidate of wrongdoing, thus preventing a riot or violence between the two sides, or you can pick a side and fight with them to give control to that side. Similar to the dwarven storyline in Dragon Age Origins.
There could be a vault that has developed a caste system where there's a previledged few who live in luxury, not having to work or contribute, and the rest live working all the time with a gun to their head (lile a Hunger Games type feel). You could try a diplomatic approach or just off those in power and set up a new system where everyone contributes and has a voice. Or you could not interfere and benefit from trading with those who are in charge.
I think the vault aspect of this game has been highly under-utelized and has so much potential. It would be cool to have these little underground off-worlds with problems of their own be a part of the Fallout 4 experience. Hopefully if they aren't they can be added in an expansion or mod.