Where is the patron saint of the Abbey of Saint Peter and Saint Paul buried?

This depends as you could be talking about either St. Peter or St. Paul, both of whom are believed to be buried in Rome. St. Peter, by tradition, is buried under the main altar of St. Peter's Basilica in Rome, where the Holy Pontiff celebrates Solemn Mass, and St. Paul is said, as of only about a decade ago, to be buried under the main altar of St. Paul Outside the Walls, also in Rome.
Sidenote- some may disagree that Rome, which I speak of as including Vatican City, is not actually Vatican City. This is true.