Whatever you put in a chest it sells at whatever value percentage the store is at. In essence you just sell your loot through this store instead of random merchants. The drawback is you have to wait a set amount of days for the inventory to clear, Maybe you have a separate side quest to draw more customers and reduce the wait time (something stupid hire a town crier to advertise or something sinister burn the competing shop in town).
I mean the same rubric could be used for food and potions (tavern) or cut out the item stocking and you own a farm. You receive funds every month but you have to complete a random side quest every now and then fight off a herd of mammoths eating crops or raiders killing the farmhands.
In the last item shop thread, I posted an idea for item shop gameplay. To bullet point it, you decorate you shop to attract a certain type of client for you to sell your loot to.
Ex: I have a lot of left over starves. Mages are willing to pay more for magic items then fighters would so I set them up fro sale then decorate my shop in crystal balls to entice mages into my store. Ex2: I have high alchemy skill and a lot of left over potions and poisons. Both mage and thieves will pay more for them, so I try to entice both of them. You get it, the game play is where pick who want what you sell to, then getting them in your store.
With an inn, you could work it the same way. decorating your inn to attract different classes, but we won't really be selling them things. If we did, it would be a shop not a inn. Actually that's all I can think of for an inn. I can't think of any more game play for it.