(This can be arranged and rearranged according to your wishes)
You can spend months exploring this beautiful country, but for the first time visit, you can do the following in 10 days:
Tehran: visit for a day. See Golestan Palace, the Tehran bazaar, Azadi tower and former US Embassy. If you have more time, you can explore modern Iran here with its parties, coffee shops, art scene and more.
Kashan: 1 day. Visit the 3 historical houses and the hammam, visit the Jameh Mosque. Walk around its narrow streets and explore the dome of its bazaar.
Abyaneh: this is either a half day trip from Kashan or a stopover on the way from Kashan to Isfahan. This red city is beautiful. You can walk around and explore its narrow streets.
Esfahan: 3 days. This is probably the most beautiful city in Iran. Marvel at the Naqsh-e-Jahan, visit its bazaars, visit the dried-up river and its bridges, listen to the locals sing at the Khaju bridge, explore the Armenian area and the Vank cathedral, visit the palaces – Hasht Behesht for instance, visit Jameh Mosque, etc.
Yazd: 1.5 days plus a day trip to Chak Chak, Meybod and Kharanaq – or visit these cities on the way from Isfahan to Yazd. In Yazd itself, visit the beautiful rooftop cafes and viewpoints and marvel at this amazing city. Visit Zoroastrian Dakhmeh and Atashkadeh, visit Khan bazaar, Amir Chakhmagh complex, watch traditional Zurkhaneh, visit Jameh mosque, Dowlat Abad gardens, etc.
If you have time, go from Yazd to Kerman, we didn’t have enough time for this unfortunately on a ten-day trip.
Shiraz: 1.5 days plus a trip to Persepolis and Necropolis. Marvel at the lights of Nasirolmolk in the morning, visit Vakil bazaar, hammam and mosque, visit Shahecheragh (if you are a woman, you will have to wear some huge horrid thing, but well), in the evening visit tomb of Hafez for the amazing spirit there, you can also visit tomb of Sayeed. Visit Naranjestan Qavam, Etam garden, etc.