After you go through the Petalburg Woods, you reach the north end of Route 104, which leads to Rustboro City.
In Route 104, you can find Wurmple, Taillow, and Wingull. Also, in Ruby and Sapphire you can find Zigzagoon. In Emerald you can find Marill and Poochyena.
Talk to the person to the left to get TM09 Bullet Seed. You can use this to teach Bullet Seed to a pokémon. The TM disappears after you use it. I recommend teaching it to Seedot, since otherwise its only attack move will be Bide until it evolves at level 14.
North of that guy, there is a tree with Oran Berries and a tree with Pecha Berries.
Go north from the berry trees to enter the Flower Shop. The girl there will give you a Wailmer Pail. You can use it to water berry trees before they have berries on them. The other girl in the shop will give you one free berry per day.
Outside, go north behind the Flower Shop. Check on the southernmost empty patch of grass to find a Poké Ball. The item in this area is a Potion.
Go south again, then go east. To the right of the sign, you find Lady Cindy, who has a level 7 Zigzagoon.
East of there, you find Lass Haley, who has a Lotad and Shroomish. In Ruby and Sapphire, they are level 7, and in Emerald they are level 6.
Go north up the bridge to find Twins Gina and Mia. You don't have to battle them, but if you want to, you have to talk to them. They will do a double battle with a Lotad and a Seedot. In Ruby and Sapphire, they are level 8, and in Emerald, they are level 6.
North of the bridge, you can go east to find Fisherman Ivan, who has three Magikarp. In Ruby and Sapphire, they are all level 6. In Emerald, they are level 5, 6, and 7.
To the right of Ivan, there is a Cheri Berry tree and a Leppa Berry tree. The old woman south of those trees will give you a Chesto Berry.
To the north, if you go to the right of the fence, you will enter Rustboro City, but you will be in a narrow path. At the end of the path, there is an X Defend, which increases defense temporarily in a battle.
That path is a dead end, so go back out of that path, then go west and north to enter Rustboro City.