Since Iran has a great diversity of ethnicity you can find different kinds of products and handicrafts in each city. You can choose to bring back to your country anything from sweets and edible souvenirs or beautiful and precious handicrafts.
If you are going to visit Shiraz make sure to take a look at traditional colorful persian carpets made by Qashqai nomads.
Other than handmade carpets you can buy many other souvenirs like Khatam, glass wares and enameled utensils and also edibles like Masqati.
Naghsh e Jahan square in Isfahan is a central place for buying Iranian handicrafts made by Isfahani artists. Main souvenirs and handicrafts of Isfahan is Qalamkar tablecloths and bed sheets and also copper engraving ornaments and statues.
Iranian caviar is the best caviar produced in the world. Also different kinds of nut like pistachio which is an exclusively Iranian fruit.