After thwarting Team Magma/Aqua's attempt to steal the Devon Parts, you get your Costume Contest and can go north to Route 110.
Explore the Route
In the grass in Route 110, you can encounter Zigzagoon, Gulpin, Wingull, Electrike, Voltorb, Minun, Plusle, and Oddish. Using the Old Rod, you can encounter Tentacool and Magikarp.
Near the start of the route, there is a building that leads to the Seaside Cycling Road. There is a vending machine inside, but you won't be able to go through the rest of the building because you don't have a bicycle. You will get one later, so be sure to come back here after that.
Go north from the building. The Team Magma/Aqua Grunts will leave to go to Mt. Chimney, which is beyond Mauville City.
You will encounter Poké Fan Isabel, who has Plusle and Minun.
North of Isabel, there is the Trick House. In the Trick House, you can go through different mazes to win prizes, such as TMs and held items. Most of the mazes require moves that clear obstacles from your path, and you don't have all of those moves yet, so you won't be able to get through all of the mazes yet.
Eastern Route 103
West of the Trick House, you can reach the east side of Route 103, which you couldn't reach before because there is water in the middle of the route. In this area, you can battle Aroma Lady Daisy, Twins Amy and Liv, Poké Fan Miguel, and Fisherman Andrew. You can get a Guard Spec in the southwest part of the area east of the water, and if you have a pokémon with you that knows Cut, you can reach some berry trees.
Back to the Route
Back in Route 110, go east from the Trick House. You will find a Dire Hit in the corner.
Near the Dire Hit, you find Youngster Timmy, who has Poochyena, Aron, and Electrike.
Go north from there and you will find your neighbor, who challenges you to a battle. If you chose Treecko, your neighbor has Combusken, Shroomish, and Wailmer. If you chose Torchic, your neighbor has Marshtomp, Shroomish, and Slugma. If you chose Mudkip, your neighbor has Grovyle, Wailmer, and Slugma.
Afterward, your neighbor will heal up your team and give you the Dowsing Machine. You can use the Dowsing Machine to find hidden items. But while you wear it, you can't sneak up on pokémon. If you are far away from a hidden item, the Dowsing Machine is blue. When you are a little closer, it's green. When you are pretty close, it's yellow. When you are standing right in front of the hidden item, it turns red and wiggles around.
There is a hidden Full Heal south of where you just battled your neighbor. There is a hidden Great Ball north of where you battled your neighbor. West of that, there is a hidden Revive.
West of the hidden Revive, you encounter Collector Edwin. He has Lombre and Nuzleaf.
West of the Collector, you encounter Psychic Edward. He has Abra.
North of the Psychic, there is a hidden Poké Ball.
To the north, you find Fisherman Dale, who has Tentacool and Wailmer.
Nearby, there is a building that leads to the Seaside Cycling Road, but all you can do there without a bike is use the vending machine.
To the northwest, there are a few Leppa Berry trees.
Go north and you will reach Mauville City.