The Milky Way galaxy does not revolve around any single galaxy. Instead, it is part of a group of galaxies known as the Local Group. The Local Group is a small cluster of galaxies that includes about 54 known member galaxies, including the Milky Way and the Andromeda Galaxy (M31), among others.
Within the Local Group, the Milky Way and Andromeda Galaxy are the two largest members. The Milky Way and Andromeda are on a collision course and are expected to collide in about 4 billion years, merging to form a new galaxy. This collision will be a significant event in the future evolution of both galaxies.
On a larger scale, the Local Group is just one member of the even larger cosmic structure known as the Virgo Supercluster. The Virgo Supercluster contains thousands of galaxies, including other galaxy groups and clusters, all gravitationally bound together.
So, while the Milky Way is not revolving around a specific galaxy, it is part of the Local Group, which itself is part of the larger structure of the Virgo Supercluster.