Basilica Cistern
Yerebatan Caddesi 13, Sultanahmet
Entrance £3.50
Open. Tue-Sun 9am-7.30pm (Apr-Sep), 9am-5pm (Oct-Mar)
http://yerebatan.com


Hagia Sophia 
Sultanahmet Square
Entrance £7 
Open Tue-Sun 9am-7.30pm (May-Oct), 9am-5pm (Nov-Apr)
http://www.hagiasophia.com

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Topkapi Palace
Sultanahmet
Entrance 20 TL (£4.65)
Open Tue-Sun 9am-6pm (harem 9am-5pm)
http://www.topkapisarayi.gov.tr/tr

Blue Mosque
Sultanahmet Square
free entrance 
Open outside prayer times
http://www.bluemosque.co


Galata Tower
 Beyoğlu
Entrance £3.50
Open 9am-8pm


Istanbul Modern*
Karaköy
Regular: 19 TL, Students: 9 TL, Groups (more than 10 People): 15 TL
Closed on Mondays, 
Open Tue-Sun 10am-6pm
http://www.istanbulmodern.org/en
*Has a great restaurant


Rumeli Hisarı
The Bosphorus strait
Entrance 10 TL (£2.33)
9am-noon & 12.30-4.30pm Thu-Tue