The Sun is not a stationary object. Our entire solar system with the sun included revolves around the center of our galaxy, the Milky Way. The Sun is located about 25,000 light years away from the center of of the galaxy. It takes 225-250 million years for the sun to complete a single orbital revolution; this is referred to as a galactic year. The shape of the Sun's orbit is roughly elliptical, but there are variations in the orbital path due to gravitational effects from other mass bodies in the galaxy.
That means we also go round our Milky way galaxy.
If so, why the distance to our neighbouring stars is always same!
The Sun's place in the Milky Way
The Sun (and therefore the Earth and Solar System) may be found close to the inner rim of the Orion Arm, in the Local Fluff, 8.5±0.5 kpc from the galactic center. The distance between the local arm and the next arm out, the Perseus Arm, is about 6,500 light-years .
The Apex of the Sun's Way, or the solar apex, refers to the direction that the Sun travels through space in the Milky Way. The general direction of the sun's galactic motion is towards the star Vega near the constellation of Hercules, at an angle of roughly 86 degrees to the direction of the galactic center. The sun's orbit around the galaxy is expected to be roughly elliptical with the addition of perturbations due to the galactic spiral arms and non-uniform mass distributions. We are presently about 8.5 kpc from the center of the galaxy and roughly 1/8 of an orbit before perigalacton (the sun's closest approach to the center, ~8.3 kpc).
It would take the solar system about 200-250 million years to complete one orbit ("galactic year"), and so is thought to have completed about 20-25 orbits during its lifetime. The orbital speed is 217 km/s, i.e. 1 light-year in ca. 1400 years, and 1 AU in 8 days.
The disk of the Galaxy is a flattened, rotating system which contains the Sun and other intermediate-to-young stars. The sun sits about 2/3 of the way from the center to the edge of the disk (about 25,000l.y. by the most modern estimates). The sun revolves around the center of the galaxy about once every 250 million years. The disk also the galaxy about contains atomic (HI) and molecular (H2) gas and dust.
The sun does revolve around the center of our galaxy, the Milky Way. It takes 225.250 million years to make one complete orbit.