After you explore Verdanturf Town and create a shortcut through Rusturf Tunnel to Rustboro City, you should go north from Mauville City to reach Route 111.
If you use the Old Rod in this route, you can find Goldeen and Magikarp. In addition, you might encounter Geodude when using Rock Smash.
To the north, there is a house where you can battle the Winstrate Family. If you win four battles in a row, you win the Macho Brace. If a pokémon holds the Macho Brace when it knocks out other pokémon, its stats will increase more when it levels up.
As you go farther north, you will see Interviewer Gabby and Ty standing next to each other. Talk to them to start a Double Battle. They have a level 19 Magnemite and level 19 Whismur. (They are level 17 in Emerald.)
Nearby, there is Picnicker Irene, who has a level 18 Shroomish and level 18 Marill. (They are level 17 in Emerald.)
Farther north, there is Camper Travis, who has a level 19 Sandshrew.
Avoid the Desert
If you go too far north, you find a desert that you can't access because of a sandstorm. Go west from the desert to reach Route 112.