After you complete Lana's trial in Brooklet Hill, you can go south from Paniola Town to Route 6.
Route 6
Southeast of the Route 6 entrance, you can battle Youngster Anthony, who has a level 15 Magby and a level 16 Yungoos. You get 320 Pokédollars for winning.
To the left of where you fought Anthony, there is a Super Potion.
Farther south, you can battle Pokémon Breeder William, who has a level 17 Sudowoodo.
If you go through the grass behind William, you find a side-entrance into Paniola Town. Check on the hay bales to the north to find a hidden Super Repel. Down below, there is TM88 Sleep Talk.
Back in Route 6, go south and you will find Hapu being harassed by a the Team Skull Grunts that have been bothering you. You will battle a Team Skull Grunt who has a level 17 Drowzee. You get 544 Pokédollars for winning.
Afterward, Hapu encourages you to visit the Battle Royal Dome, you can go east into Royal Avenue, or you can finish exploring Route 6, which leads to Heahea City to the south.
If you go south in Route 6, you can battle Beauty Brittney, who has a level 17 Cubone. You get 544 Pokédollars for winning.
If you go to the left of the Beauty, you can use your Tauros to break the rocks and get a Rare Candy.
If you go through the grass south of those rocks, you can find a hidden Carbos.
To the right of where you found the Rare Candy, you can battle Dancer Maika. She has a level 17 Oricorio. You get 680 Pokédollars for winning.
In the grass to the right of Dancer Maika, there is a hidden X Speed.
Eastern Heahea City
If you keep going south, you will reach the eastern part of Heahea City, which you couldn't reach before because a guy on a Stoutland was blocking it.
While you are here, you can visit the Dimensional Research Lab, although you can't do anything in the lab right now. There is a green sparkle in front of the lab that you can collect in the Zygarde Cube. To the right of the Dimensional Research Lab building, there is a narrow path that leads to a Big Mushroom.
To the left of the Dimensional Research Lab, there is an office building. The Game Freak office is on the second floor. Talk to the girl in the upper-left of the Game Freak office to get a Lemonade. You can get Fresh Water from the vending machine.
On the third floor of the building, you find an Aether Foundation office. The people there look like the ones that were chasing Lillie in the cutscene at the beginning of the game...
South of that office building, you will find Diglett's Tunnel. If you go in, you find Olivia talking to a couple of Aether Foundation people. But you can't go farther into the tunnel yet.
For now, go north through Route 6 to reach Royal Avenue to the east.