Ben 10,000's Headquarters is Ben 10,000's base of operations as well as his home.
The first headquarters was located in Omnitrix City, near Mount Rushmore. A large statue of Ben 10,000 was built at the center of this headquarters.
In Ben 10,000, this headquarters was where 10 year old Ben met his future self. It was the center of the episode and featured the fight between the Bens and Vilgax.
It also stores ancient alien artifacts Kai's family collected over the years. (Such as Excalibur). It had a Chronoporter which could teleport people to different times and places.
Another version of the Headquarters was first shown in And Then There Was Ben when the other Good Bens came to recruit Ben 10,000 to the fight.
It was again shown at the beginning of The End of an Era, where it featured Ben's and Kai's fight against Animo.
Ben 10: Omniverse