The Karate Building is located in Saffron City in the Kanto Region. It is called the Training Dojo, and is right next to the Sixth Gym. If you have Janine's phone number, you can battle her in there.
Mt. Mortar
He is in Mt. Motar
breed a hitmonchan/hitmonlee/hitmontop or find the karate master in mt.mortar
The Karate King is in the basement of Mt. Mortar, East of Ekruteak in Gold, Silver, Crystal, Heartgold, and Soulsilver. He has a Hitmonlee and Hitmonchan, and will give away a Tyrogue upon defeat.
Saffron City
at kanto in saffron city
The Silco Building is in the NW part of Celadon City in Kanto.
It's in Mahogany Town. Middle building.
A building in the bottom right of cerulean
In Kanto, there is a building where the Game Freak staff is. You can find the "director" in that building.
Im almost sure that it´s in celadon city, the tallest building
If you have battled him he will give you a tyroge then nothing more happens