Yes, there is a point in the universe where everything appears to spin around that point, and it is called the "Cosmic Microwave Background (CMB) dipole." The CMB dipole is a phenomenon observed in the cosmic microwave background radiation, which is the residual radiation from the early stages of the universe.
The CMB dipole is caused by the motion of the Earth and our local group of galaxies through the universe. As the Earth orbits the Sun, the Sun orbits the center of the Milky Way, and the Milky Way moves within the local supercluster, this collective motion creates a reference frame against which the cosmic microwave background can be measured.
The CMB dipole indicates that there is a specific direction in the universe from which the radiation appears slightly blueshifted (coming towards us) and another direction from which it appears slightly redshifted (moving away from us). This is a result of our motion relative to the rest of the universe.
However, it's important to note that the concept of a stationary or central point in the universe is somewhat misleading. The universe has no fixed reference point around which everything revolves. The motion we observe is relative, and different observers in different parts of the universe would have their own reference frames and perceive different motion patterns. It is the collective motion of objects at different scales that leads to the observed phenomena like the CMB dipole.