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in a chest deep in the forbidden forest
you get the card key for the radio tower in goldenrod by saving the director from the underground basement. Talk to him and he should give it to you.
Find the key
I think that you find it somewhere in Goldenrod City Underground, after that you can save the Director. All you need is a Basement Key for G/S/C.
use the basement key in goldenrod city. the key is in goldenrod.
In the north of the city, west from the gym (next to the Name Rater's Tent)
You go to the Underground area of Goldenrod and go to the door that was locked. Then you save the Director of the radio station.
If I remember correctly, once you beat Petrel, he gives you a key to get to the director, who is in the underground. The director will give you the key card.
In case in goldenrod city take the underground path. There will be a door. Get the key from the rocket executive in radio tower. In case of lavender town we can't go underground.
The card key in Pokemon Heartgold and Soulsilver is located in the Goldenrod Underground.
In order to get the Card Key in "Pokémon HeartGold," you need to get to the Director who will be in the Underground Tunnel in Goldenrod City after Team Rocket has taken over the Goldenrod Radio Tower. The Director will give you the Card Key which will open up a Card Key door in the Radio Tower which will assist you in defeating Team Rocket.
i think opens some doors in the radio tower or in the undergroun area in goldenrod city