Souvenirs can be bought at Marche Capital or Marche Sixieme in Nouakchott, or at tourist shops in the Adrar. Fabric will be sold in boutiques all over the country, but Kaedi is famous for its tie-dying.
In general, the quality of most Mauritanian souvenirs is not as good as one might expect. That said, you can find leather products, pipes, wooden bowls, tea pots and silver jewellery among other things be careful with the quality of jewellery. Fabric, however, is tie-dyed by hand and can be quite beautiful. Fabric will be sold as a mulafa veil--usually gauzy and one piece--or as material for a boubou, with two separate pieces for a skirt and top. Fabric is sold anywhere for anything from 1500 UM to 8000 UM, depending on the fabric quality and work involved.
When buying anything in Mauritania, feel free to bargain. Sometimes the starting price will be three times the actual price. Stay friendly, but don't worry about insulting anyone by asking for a lower price.