Esfahan, Shiraz/Persepolis and Yazd are absolute must-sees. A tea and a narguileh in a little cafe overlooking the dome of Sheikh Loftollah's mosque (Imam Square: Maidan-e-Naghsh-e-Jahan), goldened by the sunset, is an unforgettable experience. Don't miss Ali Qapu palace, Imam Mosque and Qaisarrieh Bazaar. Si O Se Pol bridge is an architectural marvel too (1602).
Don't miss the zoroastrian Towers of Silence in Yazd. The Zoroastrian cult, founded by Zarathustra, survives in Yazd.