In astronomy, in the galactic coordinate system, the Sun is the center. North is above the galactic plane and south is below the galactic plane. East is right of the sun, and west is left of the sun.
To be exact, East is right of the galactic core as viewed from the Sun. "Right of the Sun" makes it sound as if the Sun were being viewed from some vantage point X, which would just leave everybody confused - especially if X meant Earth (in which case the system would wobble madly against the galactic backdrop)!
This system is somewhat unlikely to be used in Star Trek for its Earth-centricity. A spherical (or cylindrical) coordinate system could just as well be centered at the center of the galaxy, with Sol merely defining the zero longitude; this is what the TNG Tech Manual suggests (going for spherical rather than cylindrical because that's what the starship-centric bearing system obviously uses, too).
According to "The Explored Galaxy" star chart, I know that Delta Vega is located near the galactic edge.
FWIW, it appears to be located near the bottom of its coordinate "cubit". So perhaps the edge being referred to is the bottom edge?
And using as a yardstick the distance from Sol to Alpha Centauri, the edge is less than 30 light years from Sol according to this chart.
Seems so (although we have to ignore the flat out incorrect positioning of certain stars in that chart to support this line of reasoning - Alpha Centauri ought to be in the direction of the galactic core from Sol, not antispinward!).
Then again, perhaps this Delta Vega we are seeing on that chart is the STXI one?
The important thing about the outer Barrier phenomenon is that it is a very thin strip. It's immaterial where in space it is - it doesn't serve as a "circumfence" in the Pratchettian sense, it's just a random line somewhere far away from Earth, and the last item of interest before one reaches the "outside" of our galaxy. But for that very reason, it defines a "rim" all on its own...
It was just too bad for the Kelvans that an approach path from Andromeda might indeed graze the rim of the galactic disk. But not exactly so; it would be much more likely for them to hit the "rim" or "edge" of a phenomenon in our local spiral arm, from slightly "above" the disk.