"My rat is full of basements. Can you clear them out?" This inverted hook made me laugh last night when I thought of it and how it might be worked up to make it plausible. More mundanely, the proprietor of a tavern named The Rat has discovered dungeons below the premises. More graphically, there is a large structure in form like a giant rat statue, or an actual enormous petrified rat, and the resident needs similar aid. If its a real, live, rat or even giant rat, you're getting into space warping or some sort of Fantastic Voyage scenario of shrinking PCs. A Tardis shaped like a rat?
I came up with a few more this morning.
"Sheep are stealing our goblins!"
Hordes of vicious elves and dwarves are ravaging the countryside. The Dragon King of Orcs needs your help to stop them.
"My hovercraft is full of eels... seriously". Alternately a location in a hex crawl, a stranded hovercraft half submerged in a swamp, and full of eels, or eel-men.
The tavern stumbles into a dying man with a map. Perhaps the tavern the PCs are in is on legs in the mode of Baba Yaga's hut?
The tomb of the undead needs protection from grave robbers.