Castle in the Sky

Castles are the place of dreams, being in plain sight but impossible for common folk to actually reach. But this trope is about castles that aren't just symbolically out of reach -- they're physically out of reach, suspended in midair.

The opposite of a Ominous Floating Castle, this represents a place to strive to reach. A Castle in the Sky may appear on a Floating Continent.

Anime and Manga

 * The Trope Namer is from Laputa: Castle in the Sky.
 * Tiphares in Battle Angel Alita might be an example too, as the place that the denizens of the Scrapyard can never quite reach (I'm reading this now, so maybe this doesn't apply?)
 * The castle in Revolutionary Girl Utena, suspended upside-down above the dueling arena, is said to be . But depending on whose interpretation you accept, it's hard to tell if it's physical or symbolic.
 * Yet another half-read example, I'm going to guess that something like this exists in UQ Holder. It certainly does symbolically in the space elevator at the capital.

Fairy Tales

 * In Jack and the Beanstalk the giant lives in one of these.

Literature

 * Castle in the Air presumably has one of these.
 * Gulliver's Travels is the inspiration of the anime Laputa: Castle in the Sky. In 'Gulliver's Travels, Laputa was an island that was able to levitate through magnetism, that was the home of both the royalty and the scholarly class.  It served as a symbol of how these groups were detached from the real world.
 * In The Phantom Tollbooth, Milo's quest is to rescue the Princesses Rhyme and Reason from "The Castle in the Air". "Rhyme: ...no matter how beautiful it seems, it's still nothing but a prison."

Theatre

 * In the 1980 musical adaption of Les Miserables, Cossette sings a song called "Castle on a Cloud" as a child. It represents her daydreaming of a place where she's loved and free from her abusive life with the Thernadiers.

Video Games

 * The castle of Queen Zeal in Chrono Trigger tops the Floating Continent of Zeal, a peaceful and enlightened land (or so it seems). That is, unless you're stuck on the Earthbound Island below
 * One of the levels in Scribblenauts Unlimited was Storybook Keep, a castle on a cloud inhabited by fairy tale characters.