Where are Star Fleet Headquarters on Earth? Does it ever tell you?
I sort of assumed that it was somewhere in North America but if you look at the gold emblem in the command centre, the globe is centred more-or-less on Japan.
Certainly, the scenery around the base would match up with it being somewhere in Japan.
You would be able to pinpoint its location by seeing where the alien fortress starts firing down at near the end of the series but the Earth just shows in those shots as a blue ball covered in cloud. No land-masses are visible.