There is an AE building in most (not all) of the zones in the game.
What Galaxy has going for it:
Arena
It's Quiet
... Did I mention it's quiet? 
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Repurposed
Ok, that is what I thought. I just haven't noticed it since it is, yes, quiet. I do like that quiet lol
Blueside, AE is in every City Zone, but not in any Hazard or Trial Zones. Originally, it was also in Croatoa, but it looked out of place, so it was removed.
Galaxy > Atlas. Why? Back Alley Brawler. Nuff said. 
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Biggest Troll on the forums? I'll give you a hint:
I just started a new character to help some friends out. Has there always been an AE in Galaxy, or is that new? I thought it was always just in Atlas.