In one of the gyms. I don't know witch one.
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In Pokemon FireRed, the badge needed to surf is the Cascade Badge. This badge is obtained by defeating Misty, the Cerulean City Gym Leader. Once you have the Cascade Badge, you can use the move Surf outside of battle to navigate bodies of water and access new areas in the game.
it's the badge from crasher wake
Hearthome's badge
there are a lot of Pokemon that can learn surf but mostly water type Pokemon can learn surf but did you know that snorelax and rydon can lean surf
The Fog Badge. obtained from Morty in Ecruteak City