Not 'Avatar', but still

 

The movie Avatar (fictionally on the planet Pandora) had rock promontories, or islands, or something unnamed by real geology, floating in the air.

While that's not possible (on Earth, at least), there are islands that float around in lakes.

Incredible footage shows boats pushing a FLOATING ISLAND around a lake

It's in Lake Chippewa, in the state of Wisconsin.

The picture below is one of many showing the boats pushing the island, so that it doesn't block the passage under the bridge.