Graystone was a city on Earth.
Post-First Robotech War
During the Malcontent Uprisings, Malcontent Zentraedi attacked Graystone for multiple months in a row. Jack Archer was assigned the task of tracking down and neutralizing the group of renegades in the nearby Ambush Hills. He discovered very few Zentraedi in the hills, despite reports, and realized that they might have been planning an attack.
Heading to Greystone, he discovered the town under lock-down, the citizens taking shelter in the Graystone Civil Center. After stiff fighting, Jack Archer neutralized the threat and was able to leave Graystone.
Later, as Zeraal's forces advanced, the Robotech Defense Force were unable to continue protecting outlying towns, including Graystone. The citizens were evacuated into Helicopters while Jack Archer (and eventually Hiro Ishi) fended off Zeraal's assault. The citizens were then taken to Base-6. (Robotech: Battlecry)
Third Robotech War
Years later, during the Invid occupation, the ruins of Graystone had been reoccupied by scavengers and refugees. The town had shrunk considerably and was almost unrecognizable due to years of decay and abandonment. The Invid Humanoid known as Locke briefly visited the town and defended it's citizens from the invaders.