Indigo Plateau is the location of the Pokémon League within Kanto and is accessible after getting the 8 badges in the region. Once there, it's a simple building with numerous areas selling items and allowing for the heal of Pokémon. Step inside, and the Elite Four are battleable.
Madam Memorial Inside the Indigo Plateau is Madam Memorial. She will teach your Pokémon any move in its learnset, including ones at a later point in exchange for Heart Scales