After passing through Fourrage Road with your new Lapras and riding on a Skiddo, you reach Coumarine City.
Explore
Go east and you will receive a Holo Clip from your neighbor, who challenges you to a battle in front of the Coumarine City Gym.
Turn on your Dowsing Machine and go north to find an Elixir hidden on a post.
Go east and into the first house you pass. Talk to the old guy in the kitchen to get a Silk Scarf.
South of this house, there is a guy at a stall selling incense. Each incense costs 9600 Pokédollars. Incense has effects if held in battle, and it also enables certain pokémon to produce special Eggs in Day Care. For more information, check out the list of incense.
The stall south of the Incense seller has a berry on it with a sign that says "help yourself." You can take the berry. You are given the option to leave a tip afterward. There will be a new berry on this stall every day.
Go east and talk to the Fisherman. He'll give you a Good Rod. If you registered the Old Rod, be sure to deregister it and replace it with the Good Rod so you don't keep using the Old Rod. If you go back to Route 12 and use the Good Rod in the water, you can find Remoraid and Clamperl.
Now go back to Coumarine City and go east from the Incense and Berry stalls, then go north to find Hotel Coumarine. The girl at the table on the left will give you a Lucky Egg. The girl in the middle room upstairs gives you a ribbon.
West of the hotel, the girl on the hill will give you a TM quiz. She'll describe a move, then ask which move she was describing. If you get the correct answer, she'll give you the TM for that move. She gives one quiz per day.
In the city, you can find Seaside Station. Go into it to find Professor Sycamore and Diantha. Sycamore believes that the bond between trainer and pokémon is the key to Mega Evolution. Diantha says that since Mega Evolution only occurs in Kalos, maybe it's related to the legendary Pokémon of Kalos.
Professor Sycamore gives you HM02 Fly. You can't use it outside of battle yet. You have to get the next Gym Badge to use it outside of battle. After you get the next Gym Badge, you can use Fly outside of battle to fly to any Pokémon Center that you have been to before. It will make it a lot easier to go back to places that you have been to.
Professor Sycamore departs, then Diantha goes toward the exit and talks about the importance of bonds, and looking for things you have in common with others. Diantha asks you to battle her the next time you meet.
To ride the monorail, talk to the girl behind the counter at the north end of the station. It's free.
When you reach the other station after riding the monorail, talk to the guy walking around to get a Metronome.
Go outside, then go west past the Pokémon Center. Use your Dowsing Machine to find a Max Repel next to the house.
Go into the Pokémon Center. Mr. Bonding is there. He gives you Befriending Power.
Go west from the Pokémon Center, then south. You'll pass a guy on a bench. Go east from him and into the farthest house. The girl in the kitchen will mimic the sound of a pokémon in your party and ask you which one it was. If you give the correct answer, she gives you a Poké Toy. She only gives one toy.
Go south from here and you reach the gatehouse to route 13. Talk to the punk to get some Black Sludge. You can optionally explore Route 13 (Lumiose Badlands).
Go north from the Route 13 gate. At the top of the hill, there is the Coumarine Gym. Don't go there yet. Go east. Get the Sky Plate at the north end of the area with the benches.
Now go toward the Coumarine Gym. Your neighbor will arrive and challenge you to a battle. Your neighbor wants to see Mega Evolution in battle, but says you don't have to use it if you don't want to.
Battle your Neighbor
Your neighbor has a level 31 Meowstic, a level 33 Kalos starter that is strong against your starter, and a level 31 Absol.