It is in The Amusement Park. Firstly talk to N and go on The Ferris Wheel with him.
Then when you come off Team Plasma will be outside. Battle N and then walk to the other building with Roller Coasters and at the end Elesa (the gym leader) is waiting. She uses two Emolga's who keep using volt switch between each other and then she uses Zebstrika. They are both Electric Pokemon. Emolga is weak to Rock and Ice and Zebstrika is weak to Ground Type Pokemon. It is the Forth Gym Badge. Hope this helped ya :)!
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The Nimbasa Gym is right of were the old one was (in black / white), past the Ferris wheel, look for the pokeball symbol on the building
there is none but in Nimbasa City (the city with the electric gym) You Can Find the HM Strength in one of the houses and there are alot of places you can go to like an amuesment park and stadiums and a musical
You can find a Sun Stone in Raimon/Nimbasa City (The 4th Gym City) The Sun Stone can be obtained from a person in the apartment left of the Battle Subway on the 2nd floor.
Lenora, the second gym leader, is found in her gym AKA the museum in Nacrene City.
defeat the gym leader in the city it is in then you can go to in it should be the city After driftvil