It is difficult to imagine the expansion of a centerless 3-dimensional space, but this web site may help:
Expansion of the universe
A 2-dimensional analogy is the surface of an expanding balloon. There is no point
on the surface that is the center of expansion. You need an additional dimension to pinpoint it.
What makes you think that the universe only has 3 dimensions? It is most likely 10 or 11 dimensional according to string theory.
Are you at all familiar with Einstein's theory of relativity? There is no universal measurement of motion. The closest we can come to a reference frame for the universe is the Cosmic Microwave Background Radiation. The local group of galaxies is moving at about 600 km/s with respect to the CMBR, and the Earth itself is moving at about 370 km/sec in the direction of the constellation Virgo.
CMBR map
So to answer your question, if you left Earth and headed away from Virgo at 370 km/sec
relative to earth, your would be at rest relative to the CMBR.