There are 24 major deserts in the world and dozens of minor desert areas.
Maine has no deserts.
Florida has no deserts.
There are no deserts in Massachusetts.
Connecticut has no deserts.
Quebec has no deserts.
Australia has many, many deserts. Its capital is Canberra. Chile has deserts. Its capital is Santiago. Egypt has deserts and its capital is Cairo. Algeria has deserts and its capital is Algiers.
No, not all deserts are surrounded by deserts.
Korea has no true deserts.
Hawaii has no true deserts.
Japan has no deserts so, therefore, it has no deserts with caves.
There are no deserts in or near Rome, Italy.
The southwestern United States has many canyons and deserts.