The inland wine region is dotted with small bodegas where you can taste locally-made wine before you buy. El Grifo , Stratvs Bodega are two of the best, both of which have gift shops selling other items, such as local art, jam made with island produce, chocolates and small gifts.
In this part of Lanzarote, the shop within the Casa-Museo del Campesino sells Cesar Manrique prints and local arts and crafts.
La Geria is in Lanzarote. For general advice on shopping in Lanzarote, see my Shopping in Lanzarote page.