Alberquerque Theater is a small theater complex that was located in New Mexico (presumably in Alberqueque), which Waylon Smithers, Jr. and a performing arts group used for a Malibu Stacy musical that he wrote, directed, and had a lead role in (due to his being a massive fan of the franchise).
Waylon Smithers, a massive fan of the Malibu Stacy franchise, had wrote and directed a Malibu Stacy musical production, and also had a major role as the titular doll's boyfriend. At some point, he and presumably the production staff were allowed to have a showing at the Alberquerque Theater in New Mexico. This likewise required him to take a leave of absence from his duty as the assistant to Charles Montgomery Burns at the Springfield Nuclear Power Plant for a week. Although Mr. Burns initially mocked Smithers for his idea about a musical based on a doll while sarcastically suggesting that they make a play about the common housecat or the King of Siam instead, he ultimately let Smithers take his leave upon learning they booked a theater at New Mexico (while being surprised that there was even a New Mexico, let alone that it was part of the United States), citing he'll keep himself amused while he was gone.
Smithers then went to the theater and performed there. It is unclear whether his musical was a success or not, although one of the male patron's remarks to his wife ("This is better than a movie … why?") implied that it was a failure.
Behind the Laughter
Alberquerque theater, and more importantly the musical it helmed, played a small but important role in the episode Homer vs. Dignity, as Smithers' attending it for a musical production he wrote and thus taking a mandatory leave of absence because of it necessitated Mr. Burns hiring Homer to be his prank monkey.
This also was one of the more controversial elements of the episode, although to a far lesser degree than the infamous scene where Ping-Ping raped Homer, due to it being one of several instances of the episode reusing old plot points, in this case reusing part of the plot for Homer the Smithers (namely, Mr. Burns hiring Homer to replace Smithers while the latter was out of town for personal reasons).
Originally, the Malibu Stacy musical subplot at the theater was intended to be longer, though for unknown reasons, it was largely cut save for a brief showing of the musical.