You find Meteor Falls after passing through Fallarbor Town and Route 114. It leads to Rustboro City.
In this area, you can find Zubat. In Ruby and Emerald, you can also find Solrock. In Sapphire, you can also find Lunatone.
Go north up the two sets of stairs to find a Full Heal. Then go back down and go west across the bridge. Go down the nearby stairs to see a scene with Team Aqua and Team Magma.
Afterward, go south and talk to the scientist. It's Cozmo. After you talk to him, go west and up the stairs to get a Moon Stone.
Go south until you get outside. You will reach Route 115. On the east side of this route, you can use Rock Smash to reach a Great Ball.
For now, just go south through the route until you reach Rustboro City. Then go east until you reach Mauville Town. You might want to go to the Bike Shop while you're there and switch to the Acro Bike if you don't have it already. It can be useful in the next part. From Mauville Town, go north to Route 111. Go west to Route 112 and go up the mountains. Instead of going into Fiery Path like last time, go northeast to enter the cable car to Mt. Chimney.