After you get rid of the Team Aqua/Magma Grunts in the Slateport Oceanic Museum, you can go north to Route 110.
In this area, you can find Oddish, Wingull, Electrike, Plusle, Minun, and Gulpin. In addition, in Ruby and Sapphire you can find Zigzagoon, while in Emerald you can find Poochyena. Also, you can use the Old Rod here to encounter Tentacool and Magikarp.
Follow the dirt path north. You will pass Pokéfan Isabel, who has a level 15 Plusle and level 15 Minun (they are level 14 in Emerald).
North of Isabel, you reach a house. This is the Trick House, where you can go through a maze to win prizes. There are also trainers in the maze.
Go east from Trick House and you will reach an area of grass. In the grass, you can find a Dire Hit. Nearby, there is Youngster Timmy, who in Ruby and Sapphire has a level 12 Poochyena, level 16 Aron, and level 14 Electrike, and in Emerald has a level 15 Aron and level 13 Electrike.
There is a hidden Full Heal in an empty spot north of the sign near Timmy.
North of Timmy, you find your neighbor and will have to battle to proceed. In Ruby and Sapphire, if you chose Treecko, your opponent will have a level 18 Wailmer, level 18 Shroomish, and level 20 Combusken. If you chose Torchic, your neighbor will have a level 18 Shroomish, level 18 Numel, and level 20 Marshtomp. If you chose Mudkip, your neighbor will have a level 18 Wailmer, level 18 Numel, and level 20 Grovyle. In Emerald, instead of Wailmer, your neighbor has Wingull, instead of Numel, your neighbor has Slugma, and instead of Shroomish, your neighbor has Lombre.
If you defeat your neighbor, you get an Itemfinder. You can use it to find hidden items.
There is a hidden Great Ball north of where you fought your neighbor. It's in an empty patch of grass near the sign north of where your neighbor was.
After you go north from where your neighbor was, go west. Check in the empty patches of grass to find a hidden Revive. In Emerald, the Revive is near the sign.
West of the hidden Revive, you will encounter Collector Edwin, who has a level 14 Lombre and a level 14 Nuzleaf. In Emerald, Guitarist Joseph is nearby and might join Edwin for a Double Battle. Joseph has a level 14 Electrike and level 14 Voltorb.
West of Edwin, you will go under the bike path. West of there, you find Psychic Edward in the grass. He has a level 16 Abra (or level 15 in Emerald). Also, in Emerald, Triathlete Alyssa is near Edwin and may join him for a Double Battle. She has a level 15 Magnemite. In Emerald, you can find an Elixir near Alyssa.
There is a hidden Poké Ball in an empty spot of grass north of Psychic Edward.
To the north, you find Fisherman Dale. In Ruby and Sapphire, he has three Tentacools (two of them are level 12 and one is level 9) and a level 15 Wailmer. In Emerald, he has two level 11 Tentacools and two level 14 Wailmers.
North of there, you will find Nanab Berries.
Continue going north to reach Mauville City.