Floating Continent: Actually, there are quite a lot of these, whether you call them skyhomes, sky cities, or sky islands (in roughly increasing order of size). They are divided into the ones which hover over terrestrial worlds (which exist mostly because people think they’re cool, and why not?), the ones which float at a more people-friendly level in the atmospheres of planets of more Venerian temperament, and the ones which float around in the atmospheres of actual gas giants. (The distinction there between “hover” and “float” is whether they’re actively powered and maintained by vector control, or whether good old aerostat principles are good enough to keep them up there.)
Not to be confused with orbital cities, which don’t float, but rather fall in endless circles.