Where is Akatsuki's headquaters located?

Answer 1

There are presumably more than one one bases through the Naruto world one in Amegakure and another around the general area between Konohagakure and Sunagakure. Though later in the story, it is revealed that Madara Uchiha has one or two extra bases only he knows of and uses.

Hope that helps :)

Answer 2

i think they have no headquarters. they just go to some meeting point or use a jutsu that to communicate to each other but you can mostly see Pein and Konan in their homeland Amegakure the Hidden Rain Village.