After you defeat Wattson in the Mauville Gym and get the Dynamo Badge, you can go west to Route 117.
In this route, you can find Oddish, Marill, Volbeat, and Illumise. In Ruby and Sapphire you can also find Zigzagoon, Surskit (very rare), and Roselia. In Emerald, you can find Poochyena and Seedot. In addition, you can use the Old Rod to encounter Goldeen and Magikarp.
The next gym is a Fire-type gym, so be sure to start training some Water-type, Rock-type, and Ground-type pokémon.
In this route, you will find the pokémon Day Care. You can leave two pokémon here, and they will level up as you walk around. You have to pay to get them out of day care. In addition, if the two pokémon that you leave in the Day Care are male and female, and if they are compatible, they might lay an egg. The egg will hatch into the lowest evolution level of the female that you left in the Day Care. If the pokémon are not compatible, the Day Care Man will say "The two prefer to play with other Pokémon than each other." Otherwise, if the Day Care Man says something different, there is a chance that the pokémon will lay an egg. You can talk to the Day Care Man to find out if your pokémon have laid an egg.
Explore the Route
Near the Day Care, Triathlete Dylan is running around. He has a level 18 Doduo (level 17 in Emerald).
South of the trees that are south of the Day Care, you find Sr. and Jr. Anna & Meg. You can talk to them to start a Double Battle. They have a level 16 Zigzagoon (level 15 in Emerald) and level 18 (level 17 in Emerald) Makuhita.
West of those two, there are Wepear Berries.
A little farther west, there is Pokémon Breeder Lydia, who has a level 12 Wingull, Shroomish, Marill, Roselia, Skitty, and Goldeen. (They are level 11 in Emerald.)
In the northwest of the route, you can use Cut to reach a Revive. South of the flower beds, you can find a Great Ball and a hidden Repel.
Go west from there to reach Verdanturf Town.