Ben 10,000's Headquarters is Ben 10,000's base of operations as well as his home.
Another headquarters was built sometime after the events of Ken 10. 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.
The new Headquarters was first shown in And Then There Was Ben when the other Good Bens came to recruit Ben 10,000 to the fight.