As souvenirs, you should definitely consider some Persian sweets as they are unique and delicious.
By far my favorite sweets are the pistachio baklava made in Yazd. The best baklava in Yazd can be found at Haj Khalife Halirahbar shop in central Amir Chakhmaq Square. Expect a long queue, because there always is, but trust me, totally worth your time.
Gaz is the nougat Persian style traditionally from Isfahan, a sweet mixed with chopped pistachios and almonds. Much sugar-based, I confess I’m not crazy about it.
Sohan among the things to buy and take home as souvenir Sohan is another type of Iranian confectionery, a Persian-style toffee with chopped walnuts and pistachios mixed in it. The city of Qom is famous for its sohan as it’s traditionally from there and considered the best.