Non-fetch quests - draw a map of an area for the local commander; investigate an unexplained phenomena in the woods, find the source of the rot in the woods and eliminate it, guard a caravan of precious macguffins to the big city, explain why the sign of the black goat is being scrawled on doors all over town, test the veracity of a local legend that says a strange tower appears in the hills every 10 years on a particular night, clear out some monsters and reclaim a manor house that has been overrun by the woods - you clean you own it, engage in a battle of wits with another party of adventurers that are in town for unknown reasons.
That's what I have off the top of my head anyway. It's no more immersion breaking than an episodic show IMO. You can do the long arcs with NPCs and village happenings - pepper the game with disputes, marriages, feuds, elections, divorces and all that jazz to bring the village to life. The more engaged the players are in the village, the less prompting they'll need to work to solve the villages problems when they come up.