Most monuments have an entrance fee except for some mosques, Shrines and gardens. It was much more expensive for foreigners some years ago (like 10times) but the tourism organization lowered them to the same price as for native Iranians.
The fare for most places is now 50 cents to 1 dollar except for the places which are not under the supervision of tourism organization like Eram garden in Shiraz (run by Shiraz Unirversity as a batonical garden).
The entrance fee is 4$ and some tourists just turn away while it is definitely a must-see place.
After all, most entrance fees are dirt cheap in Iran. so you shouldn't worry about that. Even the few exceptions are worth visiting. Some sites can be visited for free like Hafez on Friday mornings.