Post-Crisis
Recently Argo is shown to still be in-continuity. In issue #6 of Supergirl, Supergirl and Power Girl travel to the bottled city of Kandor. There Supergirl claims that the city of Argo still exists, and that she is searching for it as it is a piece of her home.
In Action Comics #869 it is revealed that before Krypton was destroyed, Zor-el and Alura used Brainiac's shield technology to create a dome over their home of Argo City protecting it for a short time after the explosion that destroyed Krypton. Soon afterwards, sensing his technology in use, Brainiac found the floating city in space and integrated it into Kandor and any "unnecessary" people in the city were killed. Superman finds the city on Brainiac's ship.
During the integration, Zor-El and Alura sent Kara Zor-El (Supergirl) to earth to find her baby cousin Kal-El (Superman).
Read more about this topic: Argo City