Assuming you came from Ten Carat Hill, make your way to the front of the shopping mall by cutting through the Beachfront. You’re looking for the big building below the Pokémon Center (to its right, if looking directly head on) that was closed earlier in the game. Inside, turn right for the sophisticated clothing store “Gracidea”.
The clothes in here are fancy alright, but the price tag might make your head spin. Best you come back after you’ve hit it big…
Moving on, head north from Gracidea via the path to the right. The first stall on the left is “Antiquities of the Ages”, which sells arcane items to be wielded by oppressively powerful Legendary Pokémon: Groudon, Kyogre, Palkia, Dialga and Giratina. After becoming Champion, you can pick up the Mythical Pokémon Magaerna here.
To the left of the Move Tutors and directly opposite the mall entrance is the weird and wonderful Battle Buffet. Here, you can pay money to fight other Pokémon trainers for food. We couldn’t make this up, even if we tried! You’ll get 10 battle turns to beat as many trainers as possible. The better you do, the better the rewards.
Last, but not least, to the left of the Battle Buffet is a stage area with seats. If it’s the day, you can watch the Alola Ride Show and receive 5 Great Balls for watching until the very end. Meanwhile, during the night, you can trigger a hilarious sidequest involving Grimer, where you can get TM48 Round.
Elsewhere in Hau’oli City
That’s the shopping mall covered, for the time being. Back outside, make your way to the town hall, directly south from the entrance of the Pokémon Center (when looking at the map). Inside, a family-to-be is causing a spectacle in front of the reception. Try to step in and you’ll be forced to fix the problem with a battle.
This pitiful Normal-type Pokémon hardly stands a chance against somebody who just beat the island kahuna. That said, you should be mindful that it knows Pursuit just in case you try to send out a Ghost-type. As usual, send it pummeling with a Fighting-type if you have one.
Triumph and you’ll receive a nugget of wisdom, as well as an actual Nugget. While you’re here, go up to the reception counter directly ahead. Say “hi” to the lady in green; a Delibird will arrive with a delivery. It’ll then pass you an unwanted Shell Bell, which restores a small amount of HP with each attack.
If you don’t mind running around some more, return to the main road, then proceed all the way towards the Marina at the far end of the city. Inside the Ferry Terminal, building, approach the woman standing near the vending machine in the top-right corner.
After seeing your Rotomdex, she’ll ask for Rotom’s help to repair the vending machine. Your reward for lending Rotom is a can of Fresh Water and a working vendine machine. There’s nothing else to do, so return towards the direction of the Pokémon Center, then continue along the road towards the exit to Route 2.