you could go the route of Avatar.
'The Hallelujah Mountains are floating islands that circulate slowly in the magnetic currents like icebergs at sea, scraping against each other and the towering mesa-like mountains of the region. On Pandora, huge outcroppings of unobtanium rip loose from the surface and float in the magnetic vortices due to the Meissner Effect'
(Meissner Effect = an expulsion of a magnetic field from a superconductor during its transition to the superconducting state).
So maybe the entire planet has ludicrously strong magnetic field, and you have some version of unobtanium? (I'm no physics major, but this seemed like the most plausible explanation for floating islands in many fantasy settings i've seen aside from 'It's magic guys!')