After Surfing across the water in Route 118, you get a legendary pokémon and the ability to Mega Evolve your pokémon. When you return, go north to Route 119.
Explore the Route
In this route, you can catch Gloom, Kecleon, Linoone, and Tropius. If you use the Old Rod in this route, you can catch Feebas, Magikarp, and Tentacool. If you use the Good Rod in this route, you can catch Carvanha, Feebas, and Magikarp. If you Surf in this route, you can catch Pelipper, Wingull, and Tentacool.
As you go north, a thunderstorm will start. (As a side note, in the real world, when thunder roars, go indoors!)
Go northwest from where you entered, and you will find a Max Repel.
Northeast from the Max Repel, you can battle Bug Catcher Greg, who has a level 29 Beautifly.
East of Greg, you find Bug Catcher Kent, who has a level 29 Dustox.
Southeast of Kent, you can find Bug Catcher Doug hiding in the grass. He has a level 26 Volbeat and a level 28 Illumise.
Just east of Doug, you can battle Bug Maniac Donald, who has a level 30 Beautifly.
North of Donald, you can battle Bug Maniac Taylor, who has a level 30 Dustox.
West of Taylor, you can battle Bug Maniac Brent, who has a level 28 Masquerain and a level 28 Ninjask.
North of Brent, you can battle Pokémon Ranger Catherine, who has a level 31 Breloom.
South of the Pokémon Ranger, use the Dowsing Machine to find a hidden Full Heal.
To the northeast, you can talk to the people in the cabin to heal your pokémon.
If you Surf across the water near the cabin, you can battle Fisherman Eugene, who has two level 27 Carvanhas, and a level 27 Feebas.
Go north from Fisherman Eugene to find a Zinc behind the tall grass.
Surf back across the water, then go north from the cabin and up the stairs. Afterward, if you go west through the grass, you will see a railing to the west that you can use the Acro Bike on to go across to the other side. Just ride to the end of the rail, then hold the B button and press up to hop to the other rails.
On the other side, use the dowsing machine and go north to find a hidden Calcium.
Use the Acro Bike to go back to the east side.
Go north from there and you will find a couple of Hondew Berry trees.
There is a Secret Spot north of the berry trees.
Go back to the south, then go up the stairs to reach the cliff. As you go north, you can have a double battle with Brains & Brawn Jael & Kael. They have a level 31 Machoke and level 31 Kadabra.
Go west from them and cross the bridge. Go north after the bridge and go through the tall grass. You can battle Pokémon Ranger Jackson, who has a level 29 Seviper and a level 29 Vigoroth.
Northwest of the Pokémon Ranger, you find a PP Max.
If you have the Mach Bike, you can ride up the slope north of where you found the PP Max, giving you a shortcut to the next area.
Otherwise, go east through the grass. If you go east past the stairs, you find an Elixir.
Near that Elixir, Ninja Boy Takashi is hiding behind a board with a tree painted on it. Takashi has a level 29 Koffing.
From the Ninja Boy, go west and up the stairs. You will find Bird Keeper Phil, who has a level 30 Doduo.
Go up the next set of stairs and go west to battle Bird Keeper Hugh, who has a level 30 Swellow.
Go north and you will find the Weather Institute. Some Grunts are blocking the bridge, so you have to go into the Weather Institute.
Go west and then north. If you keep going north, you will find some beds. You can rest your pokémon by sleeping in one of those beds. You can also switch your pokémon using the nearby PC.
Go east from the beds and you will encounter a Team Magma/Aqua Grunt that has Mightyena and Golbat.
If you go north from there, you will find another Team Magma/Aqua Grunt. In Omega Ruby, the Grunt has Koffing. In Alpha Sapphire, the Grunt has Grimer.
Go east and then up the stairs. After a brief scene, go south and you will battle a Team Magma/Aqua Grunt. In Omega Ruby, the Grunt has Numel and Mightyena. In Alpha Sapphire, the Grunt has Carvanha and Mightyena.
Go south. You can avoid the next Grunt by going around the table to the south. The Grunt has Golbat.
Afterward, go west and you will fight the Team Magma/Aqua Admin.
In Omega Ruby, you battle Tabitha, who has Camerupt.
In Alpha Sapphire, you battle Shelly, who has Sharpedo.
After the battle, the researcher will give you Castform. If you don't have room in your party, use the PC downstairs.
Go downstairs and talk to the researcher near the vending machine to get a Rocky Helmet.
Talk to the receptionist to get a random weather-related rock. Talk to her again each day until you have all four weather rocks.
Go outside and go east across the bridge that Team Magma/Aqua had been blocking. After the bridge, go south down some stairs. You can Surf north and get out of the water to the right of the waterfall, then use the Dowsing Machine to find a hidden Max Ether.
There is a Secret Spot to the left of the waterfall.
Surf south from the waterfall and get off on a patch of grass to the east. Use the Dowsing Machine there to find a hidden Ultra Ball.
Surf farther south to find a couple of Secret Spots and a Leaf Stone.
Go north and your neighbor will appear and challenge you to a battle.
Battle Your Neighbor
If you chose Treecko, your neighbor will battle you with Combusken, Shroomish, and Wailmer.
If you chose Torchic, your neighbor will battle you with Marshtomp, Shroomish, and Slugma.
If you chose Mudkip, your neighbor will battle you with Grovyle, Wailmer, and Slugma.
After the Battle
Afterward, your neighbor gives you HM02 Fly. You won't be able to use it outside of battle until you get the next Gym Badge, but that will be soon.
Go north from where you battled your neighbor. There is a Ninja Boy hiding near the top of the stairs. It's Ninja Boy Yasu, who has a Ninjask.
Go north from there to find a Secret Spot, as well as some Pomeg Berry trees to the west.
That is all that you can reach right now in Route 119, so continue east to Fortree City.