I have started doing some research the following is a possible tour recommended on TA
Day 1
Topkapi Palace and Harem – Entrance Fee
Hagia Sophia Museum – Entrance fee
Blue Mosque
Basilica Cistern – Entrance Fee
Day 2
Grand Bazaar
Suleymaniye Mosque
Galata Bridge – Fish Sandwiches as shown on Allegr’s Turkish Delight Cookery program
Galata Tower – Entrance Fee
Day 3
Dolmabahce Palace – Entrance Fee
Istikial Street
Bosphorus Cruise - Fee
The following gives closures of these sites plus others.
Mondays:
Hagia Sophia, Archaeological museum, Turkish & Islamic Arts museum, Dolmabahce palace, Beylerbeyi palace, Rumelihisari Fortress, Mosaics museum, Military museum, Naval museum, Santralistanbul, Rahmi Koc Industry museum, Sabanci Arts & Calligraphy museum, Yildiz Palace
Tuesdays:
Topkapi palace and its Harem, Military museum, Naval museum
Wednesdays:
Chora church, Sadberk Hanim museum
Thursdays:
Dolmabahce palace, Beylerbeyi palace, Yildiz Palace
Sundays:
Grand bazaar, Spice market. Also, these Bazaars are closed on religious holidays.
All mosques (including Blue Mosque) are closed during prayers. Check the following site for prayer times which change according to the sun.
http://www.namazvakti.com/Main.php?WSLanguage=ENCurrent 2012 Museum Fees
Archeology Museum - 10 Lira
Basilica Cistern (Underground Cistern) - 10 Lira
Beylerbeyi Palace - 20 Lira
Blue Mosque - Free of Charge
Chora Museum - 15 Lira
Dolmabahce Palace - 30 Lira
Hagia Sophia Museum (St.Sophia) - 25 Lira
Miniaturk Museum - 10 Lira
Mosaic Museum - 8 Lira
Panorama 1453 History Museum - 10 Lira
Topkapi Palace (Main Entrance) - 25 Lira
Topkapi Palace (Harem Section) - 15 Lira
Turkish and Islamic Arts Musuem - 10 Lira
You can buy a Museum Pass that will get you into some of the above(Marked in bold) for 72 lira and lasts 72 hours from first use and also give discounts at other places.
I will add more as I find it.