All ranges of accommodation are available, with the highest class hotels available only in Nouakchott and Atar. "Auberges" and Campsites can rent beds/mattresses for as little as 1500 ouguiya in the Adrar and Nouadhibou.
There is usually at least one hotel in the regional capitals in the rest of the country, although they can be expensive for what you are getting. If possible, make friends with a local and try to get invited to stay with their family. As long as you don't mind a)sleeping on the ground on a foam mat b)sleeping/eating near animals or c)using a latrine, you will probably end up having a nice, memorable stay.
Hotel EmiraAvenue de Nouadhibou 2e carrefour, BP 3176, Nouakchott