Mykonos (ミコノス,Mikonosu?) is the place where Nagi used to live in during her early childhood. It is here that Nagi started hating going outdoors because she was constantly being targeted by the Mafia.
In Radical Dreamers, while Hayate and Nagi were strolling in Mykonos, Nagi's hat got blown off by the wind. When Hayate went to get it he had somehow traveled back in time and met a much younger Nagi, being the Nagi that used to live in Mykonos. Shortly after their meeting she got attacked by the Mafia but Hayate promised to protect her. They outran the Mafia but one of them was able to get near enough to get a shot at Nagi. Hayate used Nagi's hat to make him miss, though Nagi's hat got damaged instead. This event would also trigger Sonia's quest for revenge against Nagi, as this was an indirect cause of her father's, the shooter's, death.
After having saved Nagi, they went to the beach to look at the stars. However Nagi's hat got blown off by the wind again. When Hayate tried to get it he disappeared as he went back to the current timeline taking the hat with him. Leaving the past Nagi bitter about his sudden disappearance and still oblivious to her savior's identity. In the current timeline; Nagi was looking for Hayate who had disappeared but it was much later during the night when Hayate returned with Nagi's hat. But the hat he had was already damaged by the gunshot which happened in the past. Nagi noticed this, and somehow realizes that it was actually Hayate who had saved her in the past though she didn't mention anything.
Sanzenin Villa in Mykonos
The Sanzenin Villa in Mykonos (三千院家別宅にミコノス島,Sanzen'in ka bettaku ni Mikonosu shima?) is the vacation home of the Sanzenin Famliy in Mykonos and used to be the place Nagi and Maria lived in. Unlike Nerima's and Shimoda's, this place is smaller than those two. Also Mykonos's has a different main building design and has an outdoor swimming pool. This place also has an underground area, and it was here that Yukariko supposedly found the King's Jewel. During their Golden Week vacation; Nagi, Ayumu, Hinagiku, Hayate, and Isumi actually explored the same place. In the underground labyrinth they found a mural containing information about the Royal Garden. It was written in the Phrygian language which only Isumi understood. She read the first part of the words written but stopped, saying that what was written was not good and told them instead to leave immediately, which they did.