1) It is really hard to pick any particular thing that stood out above other things in Iran but historically the ancient city of Persepolis was the most mind-blowing place that I visited during my time in Iran. The earliest remains date back to 515 BC and the integrity and perfect preservation of some of the remains was beyond my comprehension.
2) Golestan Palace is a complex of several amazing buildings set around a beautiful garden in the middle of Tehran. Entry is 150,000 Rials and then it costs 50,000 for each additional building after that. The exteriors of the buildings inside the garden are beautiful mosaics, colorful and extravagant. I only entered two of the buildings and was completely blown away by both. It is up to you to decide if you want to go into all and if Tehran is your only destination then maybe it is a good idea but if you are heading onto Shiraz or Isfahan then maybe one or two are enough. Personally, I would recommend the Emarat-e Bagdir building.
3) Imam Square is an amazing area located in Isfahan. It is probably one of the places that you can’t miss along with Persepolis. It is a beautifully manicured garden complete with fountains that are surrounded by the most incredible buildings I saw the whole time I was in Iran which is really saying something. The two main ones were the Sheikh Lotfollah Mosque and the Shah Mosque. There is also an amazing ancient bazar attached to the square which is completely worth checking out!
4) From the outside, Nasir al-Mulk Mosque in Shiraz looks like a pretty normal place of worship. The entrance is done in the normal incredible Persian fashion but once you enter there is almost an entire wall of stained glass windows that create a mind-blowing explosion of colors filling the entire room, That coupled with these amazing pillars spiraling up and then arching into a brilliantly intricate tiled ceiling make it another almost impossible to miss site in Iran.
5) Vank cathedral in Isfahan was the only Christian building I visited whilst in Iran but in typical Iranian fashion, I was once again left breathless upon entry. Construction of the Holy Savior Cathedral was first initiated in 1606. The cathedral was dedicated to Armenian deportees that were resettled in the hundreds of thousands. It has a completely different fashion to any of the mosques I visited but the intricacies and details were still on another level. If you are in Isfahan which you should be then this should be high on your list!
6) Darband was actually something we stumbled across getting lost trying to find a palace. We turned the wrong way and just started walking and after a short climb uphill we found ourselves nestled into a mountain surrounded by small market stalls, restaurants, and a lake. We walked through all this initially looking for the palace, when we realized we had made a mistake we were already quite high up the mountain so we decided to hike for another hour or so towards the top. When we stopped we were greeted with a pretty amazing view of Tehran and found ourselves amongst an amazing mountain range. On the way down we stopped and bought traditional sweets and food. It was a really beautiful area not far out of the city and a nice place to get away from the fast pace of the city.