>How do you get away from all gravity? Aren't you subject to gravity from all other matter in the universe at all times?

Yes. But the effect of the distortion of space-time that we call "gravity" is subject to the inverse square law[0].

This means that, as Newton described: "The gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation distance. The force is always attractive and acts along the line joining them"

As such, while objects are affected by the distortion of space-time, the effect is diminished (but not eliminated) by increased distance from the mass that's distorting space-time.

Or at least that's how I understand it.

[0] https://en.wikipedia.org/wiki/Inverse-square_law