Galaxies do orbit around something. In fact, everything in the universe is orbiting something else. Galaxies are gravitationally bound to other galaxies, forming structures called galaxy clusters and superclusters.

Within these clusters and superclusters, galaxies orbit around the center of mass of their respective group. For instance, our galaxy, the Milky Way, is part of the Local Group, which is a galaxy cluster containing about 50 galaxies, including the Andromeda galaxy. The Local Group is orbiting within the Virgo Supercluster, which contains thousands of galaxies.

On an even larger scale, superclusters are thought to be part of filaments and voids, forming a cosmic web-like structure. Within this web, superclusters orbit around other superclusters, and so on.