Sultanahmet Mosque ( Blue Mosque ) is one of most beautiful sightseeings in Istanbul. So you can be curious about ticket price of museums in Istanbul and learn each museums fees. But Blue Mosque is not a museum, it is a place of worship to muslim people. So enterance of Blue mosque is FREE to tourists or anybody in the world 🙂 you do not have to pay anything for entering mosques in Turkey. If you see some tip boxes around doors, they put them to collect charity, they take that money to use expenses of mosque.
Do not forget to read information on doors, Tourist entrance is near of mosque different than other people, because women need to get scarf from attendants. After your visit , you will give it back.