Cinnabar island, but first you have to go in the pokemon mansion and go to the top floor and get the key. That's why it says the doors are locked at first. (WARNING! You have to know about pokemon, because there are quizzes. Get them right, go to the next room, wrong, challenge a trainer.)
If you mean the old man gym leader, go into pokemon mansion and if you keep looking around you will find a key. If you go to the gym you can use the key to get into the gym. ;)