Pokémon Ruby and Sapphire/Fallarbor Town

The Pokémon Center and Pokémon Mart are at the entrance to the Town.

Inside the Pokémon Center, you'll meet Lanette. She designed the Pokémon Storage System.

To the west of the Pokémon Center is a Contest Hall. You must have the Normal Rank to compete here. In Emerald this is another battle Hall to fight in.

In the southwest is Professor Cozmo's house, if you return with the Meteorite from Mt. Chimney he will give you TM27 (Return).

There is a hidden Nugget in the crater next to the professor's house.

Move Tutor
The house next to the Contest Hall belongs to the Move Tutor. He will teach a move to your Pokémon for a Heart Scale. You won't get any of those until you go to the bottom of the ocean and/or steal from Luvdisc later, but make sure you return to him. The Moves he teaches you are the natural moveset of your Pokémon at the present level it is. Also, some Pokémon, like Blaziken and Meditite have hidden moves that can't be learned by leveling up, but is part of their natural moveset. These moves can only be taught by the move tutor.