Visit the Hagia Sofia (devine wisdom) church. This church (turned into a mosque by the Muslims) served as a major influence for the Blue Mosque, standing right across the street, and for a lot of other mosques built all over the Turkish empire.
Get a shoe shine
You'll see a lot of shoe shine stands, sometimes in groups. The one pair of shoes I brought were a pair of comfortable black leather shoes. They were trashed when I brought them and the rain on Friday and walking through puddles and muck over the next couple of days had taken their toll. I finally broke down and grabbed an open chair in the small square opposite the ferry station in Kadikoy. A very nice and colorful older gentleman gave my shoes an expert shine in 5 minutes for all of 3 YTL. What a deal! And a great way to interact with the local culture.
It' s fantastic
You should be prepared. Before you enter the church, buy a book in your language (10 liras, it's sold by merchants near the entrance) and use it as a guide. Wikipedia or general travel books miss the details.
The mosaics are real masterpieces, and moreover they are the best-maintained mosaics of the Byzantine art. They describe the live of Mary in a way similar to today's comics, in 54 "stripes", starting from the meeting of her parents and ending up with her death. In between, we see parts from the life of Jesus.
About getting there: It's a bit complicated by public transport. We went by taxi from Beyoglou and paid 9 liras on a day with enough traffic. Just tell the driver the name in Turkish: "kariyE muzEsi".
Conclusion: Don't miss it, but don't forget the book describing what you see.
Beyazit tower (Beyazit Kulesi)
You will find the Beyazit Tower close to Suleymaniye Mosque. It is actually withing the walls of the Istanbul University - in the courtyard.
I am still not sure if it is alowed to go trough the gates of the university if you are a tourist. There is a soldier sitting there and stopping the tourists from getting into the courtyard of the university. But when I explained that I just want to take a picture of the tower he let me in. Then a group of Americans asked him to do the same as me and he refused. So, the bottom line is that if you want to have a closer look at the tower and get a picture you should try your luck and see what happens :)
Some history and facts:
Two earlier timber fire towers were swallowed up by flames, but the present Beyazit Tower made of stone bas survived since 1828.
Standing in the midst of the old quarter of Istanbul, it is still used as a fire tower today as in the past. The tower is 85 meters high and bas a total of 256 wooden steps.
The architect was Senekerim Balyan, one of the renowned architectural dynasty, and he replaced an earlier wooden tower built by his brother Kirkor Balyan.
In 1909 the tower was struck by lightning during a storm, but suffered no serious damage.
Until 1972, the tower was open to the public, but had to be closed to all except fire brigade personnel when the staircase proved unsafe.
Today, the tower is also used to give a weather forecast for the following day. A green light means rain, a red light snow, a yellow light fog, and a blue light sunshine, At night, between 04.45 and 06.00 when the Ataturk and Galata bridges are closed to road traffic to let ships in and out of the Golden Horn, the ships are guided by lights on Beyazit Tower. A green light means that ships in the Golden Horn can sail into the Marmara Sea, and a red light that ships in the Marmara Sea can sail into the Golden Horn. Two red lights mean that the bridges are closed to shipping.
great spices/herbs, friendly vendors
My Istanbul based American friend took me to this, her favorite shop in Misir Carsisi (Spice Market) this summer. They had an array of wonderful spices, herbs, dried eggplant and dried okra strung like leis that were hanging over us. My senses were engaged as I was surrounded by these wonderful aromas and the sight of deeply hued spices. We had tea and water too which were readily offered to us. Despite the name which means 'corn', you should buy all kids of spices plus dried okra, pre-mixed garam masala, Turkish saffron (safran), and the item I was hunting down, cocoa butter! 3 YTL for a good sized container of Turkish saffron, best prices in all of the bazaar.