The next day, Hau will come over to pay you a visit. He'll give you the Z-Crystals for the starter Pokemon you didn't pick: Decidium for Decidueye, Incinium for Incineroar and Primarium for Primarina. Useful if you get the starter Pokemon from a trade.
He'll also mention something about a Battle Tree. Apparently it's a place where strong trainers hang out deep in Poni Island. Sounds like our next destination then. As you step outside though, somebody will give you an Enigmatic Card and tell you to give it a look...
As you can see, after becoming Champion, there's still plenty for you to do in Alola. Of course, you can continue to train your Pokemon, battle with your friends in real life and steadily fill up that Pokedex.
To add to that, there are numerous new sidequests, to unlock new items and powerful Pokemon, and even a couple of new places to visit, most notably the other half of Poni Island, leading to the aforementioned Battle Tree.
For the most part, you can do these sidequests in any order you'd like. However, if you intend to explore the rest of Poni Island, you'll need to tackle the areas there somewhat sequentially. In any case, pack your bags because more adventures await!