Last Desert

A perhaps imaginary place, mentioned by Bilbo to exist in the extreme East of Middle-earth. In that case it lays east of the Sea of Rhun, maybe where the Hildorien once was (according to the map of Arda drawn by Tolkien and Fonstad). It was believed that the wild Wereworms lived there.

Even if this place is legendary, it shows some slight geographic knowledge on behalf of the Hobbits and other peoples of the Westlands who anyway never travalled to deserts.