There is an inn in every village on THE DOG Island, excluding Pupsville where you have your house to use instead. You can stay at an inn for 1 Woof. Doing this will give you your health back as well as cure poison.
All the inns have a nameless dog standing behind the counter where you can't reach them. Most have another dog randomly standing around in the room where you can speak to them. There will always be a dog behind the counter, and this is the one to talk to if you want to stay the night.
The only time when you can stay at the inn for free is when Henry wants you to wait while he does his painting, and he books a room at the Rune Village inn for you.
All the inns have treasure boxes where you can place your items, as well.