Our solar system, including the Sun, planets, and other celestial bodies, indeed rotates around the center of the Milky Way galaxy. This rotation is part of the overall motion of our solar system within the galaxy.
The Milky Way galaxy is a large spiral galaxy, and our solar system is located in one of its spiral arms, known as the Orion Arm or Local Spur. It takes approximately 225-250 million years for our solar system to complete one orbit around the galactic center, which is a journey of about 25,000-28,000 light-years.
In addition to the rotation around the galaxy, our solar system also moves through space. The Milky Way, along with numerous other galaxies, is part of a larger structure known as the Local Group, which includes several dozen galaxies. The Local Group itself moves within the even larger cosmic structure called the Virgo Supercluster.
This means that our solar system is not stationary but is in constant motion, both in its orbit around the Milky Way and as part of the larger-scale movement of galaxies through the universe.