This is a different kind of RPG.
You are challenged to get through the entire game with no inn!
Of course, if you're stuck, and really can't go further without an inn, you can always touch Pinkie.
There are four ways you can regenerate HP and SP without an inn.
1. After every battle, you regenerate 5 HP and 1 SP. That means you need to choose and fight your battles carefully. If you lose too much after a battle, you may want to reload your previous save and try fighting a different glitch (monster) or fighting with a different strategy or equipment.
2. From food items you find on the ground. Notice that you use these right away. They don't go into your inventory. So only step on them when you really need them. Also, be on the lookout for hidden places, that may contain bonus food items.
3. Later in the game, there will be a few healing items you can buy in limited quantities.
4. As you gain levels, some of your characters will gain healing skills, which essentially allow you to trade SP for HP. Also, one of your characters gains the ability to make carrots, which have healing properties.
I've really been enjoying figuring out how to do this resource management puzzle on all the different difficulty levels. I hope you will too.
(Edit: Ooops, I forgot to mention carrots.)