After you pass through Route 110 and receive a Dowsing Machine from your neighbor, you reach Mauville City.
Enter the City
Go north and you will find Wally and his uncle. Wally rushes off to the Mauville City Gym, which is straight ahead. If you go to the Mauville Gym, Wally will ask you to battle his Ralts, so if you are not ready, don't go up there yet. You can always say No when Wally asks, if you would rather battle him later.
There is an X Speed behind the map near where you first saw Wally and his uncle.
About Mauville City
Mauville City is huge: it has three levels. You are currently on the first floor, where there are many shops.
The second floor can be accessed from the stairs on this floor. There are also elevators in the north part of the first floor that can go to the inner apartments of the second floor, but you can't use those elevators right now, so you'll have to wait until you are authorized to use those elevators if you want to check out the Mauville Hills apartments.
The third floor is the roof, where you can get a few items.
Mauville City 1F, Courtyard
North of where you saw Wally, there is a Courtyard. This is where you can find the Pokémon Center and Poké Mart.
There is also a hidden X Defense in the Courtyard behind the statue.
Talk to the Backpacker in the Courtyard to get a Globe for your base. Don't worry if you don't know what a base is. You'll find out soon.
There is a Roselia in the courtyard that you can look at with the DexNav. When you do this, Roselia gets added to your Pokédex as a pokémon that you have seen but not caught.
Be sure to talk to the old guy in the Pokémon Center and listen to his story. He'll give you Speed Power Lv. 1. Listen to him again to get Critical Power Lv. 1. You can use these O-Powers in the PSS (the tab in your PokéNav Plus with three black lines across it).
Say yes to the girl in the Poké Mart to get TM58 Sky Drop.
The Poké Mart has a TM seller, but they all cost 10,000 Pokédollars, so you probably can't afford them yet. But if you can, you might want to buy TM78 Bulldoze, because it's a Ground-type move, which will be helpful in the Mauville City Gym, which is an Electric-type Gym.
Mauville City 1F, South
The south part of Mauville City's first floor has the entrance to the Mauville Food Court. Right now, only Village Sub Combo is open. When you order from there, you will be challenged to single battles. You win a Nugget if you defeat a trainer in the right number of turns, and if you defeat all the trainers in exactly five turns, you get a random rare berry.
Mauville City 1F, West
The west side of Mauville City's first floor has many shops, as well as people who give you items.
The woman behind the counter gives you TM48 Round.
There is also a Move Tutor here who can teach moves to Keldeo and Meloetta, if you can get them. They are event Pokémon that first became available in Pokémon Black and White.
Mauville Game Corner Owner
Talk to the Mauvile Game Corner owner and say that you can take the prizes. You will get several dolls for your base.
Talk to the mirror shop owner and she mentions Tornadus, Thundurus, and Landorus. If you have any of those pokémon, bring them to the mirror shop and talk to the owner.
The Ribbon Shop is across from the Mirror Shop. When you buy a ribbon, it gets added to your lead pokémon's ribbons. You can see the ribbons in the Summary page of a pokémon by tapping the third button in the bottom-left part of the screen. The ribbons are expensive, though. They are just for collecting; they don't have any effects.
At the PokéMileage Shop, you can exchange your Poké Miles for items. You can earn Poké Miles by trading pokémon with other players, meeting players with StreetPass, and in other ways. The amount of Poké Miles that you earn by interacting with other players depends on the distance between the regions that you have set in your 3DSes. The farther away those two regions, the more miles you earn from the interaction.
At the Reflexology Center, one of your pokémon can get a free massage, increasing its happiness. You can only get one massage per day.
Mauville City 1F, East
The east side of Mauville City has more of a focus on battles.
Pledge Move Dojo
Bring a starter pokémon here to teach it combo moves that can be used in Double or Triple Battles.
Ultimate Move Studio
Bring a fully-evolved starter pokémon here to teach it an Ultimate Move.
Inverse Battle Stop
You can participate in Inverse Battles here. In an Inverse Battle, type effectiveness is reversed. For example, normally a Water-type attack is super-effective against a Fire-type pokémon, but in an inverse battle, a Water-type attack will be not very effective against a Fire-type pokémon.
On the other hand, moves that aren't very effective will be super-effective in an Inverse Battle. For example, a Grass-type attack is normally not very effective against Fire-type pokémon, but in an Inverse Battle, a Grass-type attack will be super-effective against a Fire-type pokémon.
Furthermore, if a pokémon is normally immune to a move type, during an Inverse Battle that pokémon will be weak to that type. For example, Ground-type pokémon are normally immune to Electric attacks, but in an Inverse Battle, the Electric-type attacks will be super-effective against Ground-type pokémon.
You can only do an Inverse Battle once per day.
You can choose up to three pokémon to participate. All pokémon will temporarily become level 20 for the duration of the battle.
The prize you get for winning an Inverse Battle depends on how many super-effective moves you use during the battle. If you don't use any, or you use moves that are not very effective, you will get an Oran Berry. If you don't use many super-effective moves, you get a Sitrus Berry. If you use some super-effective moves, you will get a random rare berry. If you do very well, you get a random evolution stone. The best prize is a Rare Candy.
If none of your pokémon's HP gauges become red during the battle, you will give you three of the prize item instead of one.
At the Battle Institute, you can get a Vs. Recorder. Use it to record your battles on the PSS and in other places. Once you record a battle, you can go back into that battle and try it again.
Later in the game, you will be able to do Battle Tests here, which are very challenging trainer battles.
You can talk to the woman in the middle and choose Download Tests to check if there are any battle tests that you can download right now.
Get a Bicycle
In the east part of Mauville City's first floor, you find Rydel's Cycles. Talk to Rydel to get a bike. You can choose either the Mach Bike or the Acro Bike, but you will be able to switch your bicycle type any time, just by talking to Rydel.
If you choose the Mach Bike, you can go back and explore Granite Cave, which is northwest of Dewford Town. The cave has a slope near the hiker who gave you the TM for Flash, and the Mach Bike is able to ride up that slope.
In addition, you can use a bike to ride on the Cycling Road in Route 110, where you can battle trainers and try to get the best time.
Read the books in the back of the bicycle shop to learn about how to use the bikes.
Mauville City, 2F
The guy in the northeast stairwell of the second floor is waiting for Genesect, which is an event pokémon that was introduced in Pokémon Black and White. If you have one, be sure to show it to that guy.
Mauville City, Roof
You can get several items on the roof. Someone is selling a Metronome, a girl will give you a Poké Toy if you say that you really love pokémon, and someone will come up to you and give you a Nugget if you walk around the roof long enough.
Mauville City 1F, North
The north part of Mauville City has TV Mauville, the TV Studio where the shows on the BuzzNav are recorded.
Also in the north part of town, you will find the Mauville Gym.
When you approach the Mauville Gym in the north part of the first floor of the city, Wally will ask you to battle his Ralts. After you win, Wally will decide to go back to Verdanturf instead of challenging the Mauville Gym. His uncle gives you HM06 Rock Smash to thank you for helping Wally have a more positive outlook.
Visit Other Routes
If you want to, you can go to Route 117 to the west, where you will find the Pokémon Day Care, where you can breed pokémon; Route 118 to the east, where you can get Stardust and a hidden Heart Scale; and Route 111 to the north, where you find the Winstrate House.
Challenge the Gym
If you are done exploring Mauville City, you can challenge the Mauville Gym and its leader, Wattson.