Once you've earned the third gym badge, you should have no language barrier difficulties getting from Hiun City to Raimon City to the north via Route 4. Once you watch the scene with Team Plasma and N there's nothing standing in your way if you want to tackle the gym right away.
If Hiun City is the New York of the Isshu region, Raimon City is the Las Vegas. Lots of items of interest:
This is the first building in front of you when you enter Raimon City from Route 4. When you first try to enter, a girl will come out and give you the Battle Recorder. The trains, clockwise from entrance are:
Blue train – Wi-Fi battle
Orange train – Multi battle
Yellow train – Super multi battle
Brown train – To Kanawa Town
Pink train – Super double battle
Red train – Double battle
Light green train – Super single battle
Dark green train – Single battle
This is the building on the west side of the Pokemon Center. When you talk to the guy, your options are Challenge, Explanation, Download, Quit. Your Pokemon have to be at least level 50 to play.
Raimon City Gym
The gym is next to the Ferris wheel in the east area of the city. After the scene with N in the Ferris wheel you can go in and battle for the Bolt badge.
Belle is standing out front when you first approach the Musical Hall in the northeast corner of Raimon City. A guy inside gives you the Goods Case and a brief tutorial on Pokemon dress up.
Little Court and Big Stadium
These are sporting venues in the northwest area of Raimon City. Little Court is in the far northwest corner and Big Stadium is to the east of Little Court.
On the west side of town there are also two nondescript buildings – in the westernmost building on the first floor the blue-haired boy gives you HM04 Strength.
In the southwest house in the set of four orange-roofed houses to theeast of the market, the move tutor will teach your starter its respective Oath move (Grass Oath, Water Oath or Fire Oath).
Homomoe Gym is located in the northeast corner of Hodomoe. Cowboy Yacon is ready to challenge you with his Ground-type Pokemon as soon as you've scared off the Team Plasma goons in the southwest area of Hodomoe.
After you've earned the Quake badge, as you exit the gym andhead west toward Route 6 Belle stops you and challenges you to a battle. When you win, she gives you HM 02 – Fly. Finally! If you want to do any breeding, you can fly back to Sanyou City/Route 3 now, since the Pokemon day care now accepts two Pokemon.
Move relearner / move deleter
-The move relearner is the girl in the upper left corner, and she requires a heart scale for her services.
-The move deleter is the man in the upper right.
Tower of Heaven
Head north a bit on Route 7 to reach this tower. Head to the top and ring the bell.
Earn the Jet Badge at this Flying-type gym.