The Red Shield Headquarters is actually a huge cruise ship. Saya and others get on the ship for the first time after Saya gives her blood to Riku. The discovery of D-base is made by Julia in the HQ lab. After Riku stabilizes and gets normal, the HQ is attacked by the schiff. They move to one of Joel's apartments there.
Later Saya and others are moved to the HQ again after David gets tipped off by Solomon about the coming attack planned by Amshel. The location of the ship was given away by Collins. It was sailing near Marseilles when a sudden invasion of Diva and Karl throws the entire ship crew into topsy-turvy. Joel VI decides to put the ship into self-destruction mode in order to bury Diva and Karl with it. However, his idea fails as Diva flees. After the ship is blown-up, Red Shield loses its base, falls apart and some of its vital members (including David) lose hope.
In Episode 26, Riku mentions that the ship have recreation like restaurant, pool and a library.