The bank should have save deposit boxes. Such as 10s a square or something.
Because of the new travel restrictions trading heavy items can be a burden. Having a purchasable spot to store items in town could be very helpful for trading while also providing an additional money sink into the game.
If you wanted you could also have chance to open safe deposit box and find misplaced sock or break a finger nail or something. Sorry couldn't come up with anything more creative than just having a safe deposit in town.