destiny islandsAs early as the first cutscene in Kingdom Hearts, we learn that Kairi's home world is, not in fact, Destiny Islands. Destiny Islands itself is a group of smaller islands accompanied by the main inlet where the main town and the school are. Upon getting to the beach, it's quite easy to row a boat over from the main island to the smaller play island(s) where most of the children spend their time. This play island is the island we see during the events of the first game, and is usually where Kairi, along with her best friends and some of the other island children (Selphie, Tidus and Wakka), can be found. Kairi's foreignness to the world is part of the trio's motivation for leaving the islands in the first place – in Riku's perspective, her arrival confirms that there definitely are other worlds out there, and for Sora, he wants to see them all, if they do in fact exist. Kairi herself doesn't have much of a motivation to go, save that her friends are, so she will too.
The reason Kairi was sent to Destiny Islands from her home world of Radiant Garden is due to its destruction. Many years earlier whilst Kairi was living with her grandmother, Aqua, a Keyblade Master, encountered her and saved her from the being attacked by a group of Unversed. Aqua realised there was something special about Kairi, and there was a light within her heart. Both Aqua and Mickey decide she must be really important, and also quite special. Aqua then placed a magic charm on the young girl, in order to send her to those who would help her and protect her should she be in danger. This charm activated when Radiant Garden was consumed by the Heartless – and unlike many of those native to it, who had to escape via gummi ship, Kairi was whisked away to the islands, to the two hearts that would protect her – Sora and Riku. Again, this charm is perhaps the reason why Kairi's heart chooses to hide within Sora's when the islands themselves are destroyed. Again, it will keep her safe.
For Kairi, the islands are her home. She voices to Sora that she's happy on the islands; she wouldn't mind seeing her home world, but that doesn't mean she would automatically stay there. She's curious about it, naturally, especially with her amnesia, but there's no clear cut desire for her to leave. Even when finding out that her home is Hollow Bastion (Radiant Garden), Kairi doesn't form any particularly attachment to it in its ruined state. When Destiny Islands are reformed, Kairi is called back there from Traverse Town, to the beach on the play islands. She's a resident of that world – where her heart belongs, so it is the reason she returns. Home is where the heart is. Destiny Islands is a special place to her – she grew up there, with her friends, and was adopted by a presumably loving family despite her mysterious past. Why would she want to be anywhere else?
Moreover, with the current branch of the game into Kingdom Hearts III, I think it's entirely possible that she will visit Radiant Garden in its restored state. But now and forever, it's Destiny Islands where her heart truly lies.