The universe is expanding at about 70 kilometers/second/megaparsec.
Hubble's law
WMAP
You would have to travel faster than this to get anywhere, but that is not difficult since gravitationally-bound areas do not expand, and the speed of celestial objects greatly exceeds the local expansion (the Milky Way galaxy has a relative velocity of about 600 km/second).
Interestingly, the relative velocity of distant galaxies can exceed c (the speed of light) since they are not traveling
through space but being carried
with it.