There are 2 headquarters in Broken Valley, for Geshniz (by Maxos temple) and Rayhun (by the starting village). There are possible quest items and set pieces in the headquarters, but nothing you need to destroy.
Look at the map. From Geshniz's headquarters, the quarry tower is to the far south east, though there is a mountain in the way, so you can not fly straight there.
There are only 2 towers above the poison gas in Broken Valley, Lovis' tower (you can land on the top level, and get down as far as the now-locked door to Lovis' throne room) and the quarry tower (the tops of the attached walls still above the gas).
