Despite the trophy description, it does not have to be overnight -- Simply using the tavern 10 times will be sufficient. Taverns are found in the larger towns; the first available one being in Orad. It will cost Rainbow Coins to use them, but they will refill each party member's hunger levels and pass time. You will always wake up at the next 6am.
You can alternate using the tavern and campfire to work towards the Camper trophy at the same time. The tavern's hunger recovery will also counteract the increased hunger from using campfires meaning you need less food for the trophy.