Sheikh Lotfollah Mosque, Iran
This mosque in Isfahan, a city said by travel writer Robert Byron to rival Athens and Rome, would be known around the world were it in most other countries. Because it is in Iran, however, it has been explored (and Instagrammed) by very few western tourists. Built in the early 17th-century under Shah Abbas I, it does not have a courtyard or minaret, making it architecturally unusual: this is said to be because the mosque was never intended for public use, but for prayer by members of the Shah’s harem.
The Foreign Office currently advises against travel to Iran, but the recent nuclear deal may well see the country's tourism industry open up to foreigners.