After you meet Arven and take in the sights from the Lighthouse, you go northwest to South Province (Area One).
Map of Southeastern South Province (Area One)
Explore the Route
Soon after you enter the route, you can talk to the trainer to do battle. Trainers in Paldea will only battle you if you talk to them; they don't challenge you if you only make eye contact.
If you talk to the trainer, you will battle Youngster Elian, who has a level 5 Tarountula. You get 220 Pokédollars for winning.
North of Elian, there is a sparkle.
When you reach the small bridge over the creek, you can check on the Pokémon hiding under the north side of the bridge to get a Gimmighoul Coin. These will be useful later. (You can't catch Gimmighoul when it is in Roaming form like this.)
Southeast of the bridge, you find an X Defense next to a tree.
If you go farther east along the creek, you find a Paralyze Heal.
You can optionally continue walking along the creek to find a beach where you can catch Wiglett, Wingull, and more.
Then go west to go back to the bridge over the creek.
Keep going west to find a TM047 Endure at the base of the waterfall.
To the north, there are three items, each of which is a Poké Ball.
Northeast of those, you can talk to the trainer to battle Zahira the Student, who has a level 5 Lechonk.
On the ledge east of Zahira, there is an Awakening.
North of that, there is a sparkle, and north of the sparkle, there is a Potion.
On the ledge north of that, there is a Poké Ball.
Optional: Explore the Eastern Area
There is a large area to the east that you can explore, but you will soon have a faster way to get around, so you might want to just go northwest to Los Platos and come back later.
If you do go to the east, you can go northeast from the Poké Ball mentioned at the end of the previous section, to find a TM047 Endure.
Southeast of that, there is an Antidote. Go northeast from there onto the ledge to find a Gimmighoul and a TM032 Swift.
Go west until you can go southwest without jumping down from the ledge, and you will find an item that is two Poké Balls.
South of that, there is a sparkle.
Farther east, there are two items that are both Poké Balls.
Southeast of those, there is a sparkle. Go south from there, then northwest to find an X Accuracy. Then go back southeast and get the TM007 Protect.
Go west and then south from there to find a Potion.
From there, go southeast to find a TM015 Struggle Bug.
Northeast of that, there is a Full Heal.
Go north to find a Super Potion if you walk past the two ponds. You can't swim, but you will be able to come back later with a way to cross the water.
Then go back south and make your way southeast, where you will find some ruins, where certain types of Pokémon can be found. In addition, there are three Gimmighouls in and around the ruined building. There is also an Awakening in the corner.
There are columns next to the ruins, and one of them has an item on top, but you will have to come back later to get it.
East of the columns, there is a TM017 Confuse Ray.
Northwest of that, you can talk to a trainer to battle Axel the Student, who has a level 7 Squawkabilly.
Go northeast to find a sparkle, then go northeast from there to find a Paralyze Heal.
Southeast of that, there is an Antidote, and to the southwest, you can find a Dire Hit, two sparkles, a Rare Candy, a TM016 Psybeam, and a TM013 Acid Spray.
Go east until you reach the cliff wall, then go northwest and you will eventually find an Exp. Candy XS.
To the west, there is a Great Ball and another Gimmighoul. West of this cliff, there is an Awakening.
If you go north from there, you can find a Gimmighoul at the west edge of the pond. Northwest of that, there are two sparkles, and a TM076 Rock Blast.
South of that, you find a trainer with a black speech bubble. This indicates that this trainer is stronger than most of the other trainers in this area. You can talk to this trainer to battle Alejandro the Black Belt, who has a level 11 Rockruff, a level 12 Lechonk, and a level 12 Makuhita. You get 1920 Pokédollars for winning.
Southwest of that, there are two sparkles and a Potion.
Now you can go west to reach the path (or use the Map to fly back to the lighthouse), and follow the path north to reach the next destination: Los Platos.