Details: After finishing the main storyline, Hau will arrive at your place the next day and tell you he's heading to The Battle Tree next in order to get stronger to defeat you, the Champion. The Battle Tree is located on Poni Island, found by going through Poni Grove to Poni Plains, Poni Plains to Poni Gauntlet, and then Poni Gauntlet to the Battle Tree itself.
Johto, Hoenn and Sinnoh each had the Battle Tower; Unova had the Battle Subway; and Kalos had the Battle Maison. And now, Alola has a similar battle facility in The Battle Tree.