Istanbul is a new modern city in which twenty meters next to the new fashioned hotel you can still see butchers cutting sheeps' heads on the streets. That's the magy of this place!
To really enjoy the city, i think it's important not to stay only in the historical centre Sulthanamet. The North of the city, Beyoglu, shows you the modern face Istanbul and the oriental part, Uskudar and Kadikoy, show you its traditional face.
When you arrive, don't hesitate to take a taxi. Like that you can ask to go on the Kennedy Caddesi to see the ruins of the old city's walls.
In Sulthanamet i would recommend to see the mosque Aya Sofya, the blue mosque, the citern, the Topkapi Palace, the Gülhane parc with its fabulous view on the Bosphorus from the tearoom Set Ustu Cay Bahcesi, the Big Bazar and the Spice Market.
To have a drink at the end of the day the hotel bar Kybele on Yerebatan Caddesi 35 is a really nice place. And do try the typical turkish drink "boza" which you can find in the bar Vefa Bozacisi on Katip Celebi Caddesi 102.
When you go to Beyoglu take the wonderful Galata bridge where a lot of people go fishing. One says that if there are a lot of fishermen of the bridge, the unemployment is high in the city. On your way let's eat a "fish in a bread" sold in one of the several small places next to the bridge.
In Beyoglu, it's interesting to visit the Galata Tower to have a beautiful view on the city. But the view is better and cheaper from the bar of the Marmara Hotel at Taksim place. If a guy of the hotel says to you that you have to go out if you don't have a room number, you can simply say that you have a meeting with your father, who has a room in the hotel.
That's really nice to walk on the Istikal Caddesi from the Galata Tower to the Taksim Place, with all the shops, all the people - the modern face of the city.
At the end of the day you can visit the beautiful Istanbul Modern museum and have a drink in the chill bar "white mill" on Susam Sokak 13.
During your trip it's really important that you can go on the Bosphorus. There are cruises which go to the North from Sirkeci or you can go to Uskudar and Kadikoy. This latter has a fabulous market.
If you like clubbing, Istanbul is a really good place with the good tech and deep house of Germany : the oriental Berlin. But in Istanbul you need expensive clothes, a big car and a lot of girls to go in the club.
Enjoy this fabulous city where people are really open and proud to make you discover their place!