The Machine
The Machine was introduced by Neil Gaiman as The Archives, an inter-planetary mechanism built on Earth by the Celestials as the Eternals home, their transit around Earth, and their resurrector.
The Machine also functions as the third-person narrator for all of the Eternals comics written by Kieron Gillen.
Olympia
First Appearance: Red Raven Comics #1 (May, 1940) (As High Olympus), Eternals #5 (August, 1976) (As Olympia)
Creators: Martin A. Burnstein, Jack Kirby
Location: Greece
Purpose: Home of the Olympian Eternals, home of the Eternal Prime.
Polaria
First Appearance: Eternals: The Herod Factor (September, 1991)
Creators: Roy Thomas, Dann Thomas, Mark Texeira
Location: Siberia, Russia
Purpose: Home of the Polarian Eternals.
Titanos
First Appearance: Captain Marvel #29 (November, 1973)
Creators: Jim Starlin
Location: Northwest Territories, Canada
Purpose: Former capital city of the Eternals before the Olympia/Polaria divide.
Oceana
First Appearance: TBD
Creators: Kieron Gillen
Location: Pacific Ocean
Purpose: A citadel for surveillance, home of Uranos' followers under Oceanus' care.
Celestia
First Appearance: Eternals: Celestia (2021)
Creators: Kieron Gillen, Kei Zama
Location: Chile, South America
Purpose: Home of the Celestian Priests, the location for Celestials to address the Eternals.
The Exclusion
First Appearance: Eternals (Vol. 5) #1 (January, 2021)
Creators: Kieron Gillen, Esad Ribić
Location: South Pole, Antarctica
Purpose: Eternals ressurection facility, the prison for Eternals who have been "Excluded".