the globe says
Algeria
Algeria reopened Saharan tourism with visa-on-arrival for organized trips — fly Algiers to Djanet with a licensed agency.
Desert camps under the Tassili plateau; town guesthouse between excursions.
The Tassili n'Ajjer: a sandstone labyrinth holding thousands of rock paintings up to 12,000 years old — herds, dancers, gods — in a desert of cathedral-sized rock arches.
The Tadrart Rouge by 4x4 — red dunes against black rock, and engravings your guide's grandfather's grandfathers knew.
October to March
Tanemmirt — thank you, in Tamahaq, the Tuareg tongue.
The Fearful Void by Geoffrey Moorhouse — the honest account of what the Sahara does to a person.
The Tadrart Rouge itself is the extension — three more days south toward the Libyan border country.
Travel is only via licensed agencies with permits — that is the law and also the safety architecture. Border zones are strictly off-limits.