Define your coordinate system. In a heliocentric system, it does not move at all.
The whole solar system is moving around the center of the galaxy at about 230 km/s. If you use a galactic-centered coordinate system, the Sun moves 114,678 kilometers in orbit around the galaxy in 8.3 minutes.
However, the galaxy is moving toward the "Great Attractor":
"Detailed observations of the galaxies around us indicate that there is superposed on the Hubble flow a large-scale streaming motion of about 600 km/s in the general direction of the constellation Centaurus.
"This mass migration includes the Local Group, the Virgo Cluster, the Hydra--Centaurus Supercluster, and other groups and clusters for a distance of at least 60 Mpc up and downstream from us. It is as if a great river of galaxies (including our own) is flowing with a swift current of 600 km/s toward Centaurus.
"Location of the Great Attractor
"Calculations indicate that ~10^16 solar masses concentrated 65 Mpc away in the direction of Centaurus would account for this. This mass concentration has been dubbed the Great Attractor. Detailed investigation of that region of the sky (see adjacent image of the galaxy cluster Abell 3627) finds 10 times too little visible matter to account for this flow, again implying a dominant gravitational role for unseen or dark matter. Thus, the Great Attractor is certainly there (because we see its gravitational influence), but the major portion of the mass that must be there cannot be seen in our telescopes."
So the Sun moves ~299,196 kilometers toward the Great Attractor in 8.3 minutes.
However, there is another frame of reference, that of the gross motion of the Solar System with respect to the cosmic background radiation field. This motion has been found to be ~371 km/s. So the sun moves 184,980 km in 8.3 minutes relative to the cosmic background radiation.
Satisfied?
--Boris