The primary base of operations for the Nihil was the Great Hall of the Nihil, located inside their territory known as No-Space. This Great Hall was made up of a wide durasteel platform that stretched for hundreds of meters, and it was enclosed by vacuum shields that formed a dome filled with breathable air.
The Nihil used the Great Hall of the Nihil as their central command during the High Republic Era. It was on this platform that they made plans for their raids and celebrated the times they were victorious.
To defend against an assault by the Jedi in 230 BBY, the Great Hall was reinforced. This proved to be ineffective, as the Jedi successfully invaded the Hall.
During the Imperial Era, specifically during the time of the Galactic Civil War, the Great Hall of the Nihil appeared to have been deserted entirely, with its wreckage drifting aimlessly through No-Space.