There is a locked door on the top-right corner of the map. There is a huge tree leading there. This door will lead you to the sword eventually. And to find the key that unlocks the door, you need to find running shoes and then go to the caves near the place where you found the magic book.
(Now that I write these things down, I sure realize how confusing this game can be. Sorry about that, I try to remember this next time I make a game!)
