The Teenage Boy Museum only appears in the episode "Mr. Krabs Takes a Vacation". In the episode, Mr. Krabs takes Pearl, and SpongeBob on a vacation, and as they passed by potential tour stops, Pearl hoped they would visit the Teenage Boy Museum.
It seemed her wishful thinking was answered when the boat pulled in front of it, but as she eagerly ran to its doors, the museum was destroyed by construction workers using a wrecking ball. And as it turns out Mr. Krabs intended to take them to the Bikini Bottom Mint which happened to be across from the former museum.
The museum is an orange building. On the top of the building it has a cardboard cutout. The cutout has a green fish with brown hair, an orange fish with black hair, and a purple fish with orange hair.
When the museum was destroyed, there seemed to be nothing in it except for an autographed photo and pieces of the Teenage Boy Museum.