General:
* Aridity
* Barrenness
* Wilderness
* Wasteland (sometimes negative connotation)
* Expanse
* Habitat
* Ecosystem
* Landscape
Physical Features:
* Sand dunes
* Canyons
* Mesas
* Buttes
* Oasis
* Dry lake bed
* Salt flat
* Rock formations
* Scrubland
Flora & Fauna:
* Cactus
* Sagebrush
* Tumbleweed
* Desert tortoise
* Roadrunner
* Coyote
Cultural & Historical:
* Nomadism
* Caravan
* Oasis city
* Archaeological site
* Ancient civilization
Metaphorical & Abstract:
* Isolation
* Solitude
* Harshness
* Endurance
* Resilience
Other:
* Desert storm
* Mirage
* Sand
* Dust
The best noun to use will depend on the specific context and the aspect of the desert you want to emphasize.