There does not appear to be any
science fiction convention [ no pun intended ] for describing
directions of movement in respect to the
galaxy. For that reason
I propose these terms:
Hubwards - To head toward the galactic core. Some would want it hubwise.
Rimwards - To head toward the rim or edge of the galaxy.
Turnward - To travel in the same direction as the revolving motion of the galaxy.
Anti-Turnward - To travel in the opposite direction as the revolving motion of the galaxy. This one was hard. What is the opposite to Turn? Standing still? That won’t do. The nearest I could find was Widdershins, but that hardly seems scientific, does it?
The first four terms are all made in relation to qualities of the galaxy - to go turnward follows an actual motion of the galaxy etc., but the next two are by necessity made from references to extra-galactic objects - i.e. The Andromeda Galaxy [ Chosen because it is the closest galaxy to ours.]
Northward - Heading away from the ecliptic on the side of the galaxy closest to Andromeda. Choosing a name for these two was hard, but I settled on using North/South notation with Andromeda serving as a [ decidedly wonky ] pole star
Southward - Heading away from the ecliptic on the side of the galaxy furthest from Andromeda.
If there are any other systems that exist, I think this would be a good place to node them, or /msg me to link to them if they have node-able names.