Perhaps as far as artwork goes, Iran is most famous for its rugs. Something that is unique to Iran, however, is khatam kari, an art form in which wooden surfaces are decorated with intricate pieces of wood, bone and metal cut into geometrical shapes. While some of them just have these designs, others have miniature paintings on them, another form of art famous in Iran. One miniature on a khatam kari box that always stayed with me was that of chogan bazi, polo, being played in Naghshe Jahan in Esfahan. You can find a khatam kari version of almost anything- tissue boxes, pencil cases, jewelry boxes, hookahs, clocks, picture frames, backgammon boards, etc. They make for wonderful gifts as they are quite typical of Iran. Chances are, if you have an Iranian friend, you have received one of these at some point. The plates and vases pictured below are also quite popular. These are made of metal and painted with geometric designs typically in blue but sometimes also in green.
While I don't remember the exact street name, in the Karim Khan Zand area by the Saint Sarkis Cathedral in Tehran, there is a street that is lined with these stores carrying beautiful khatam kari, gelim, small rugs, and other traditional handicrafts. Of course this is not the only place. You can find these stores in many places, and even if you still need more at the last minute, there is always the duty free store at the airport.