Wow,
So much to comment on just from what has already been mentioned.
Rugs: Difficult subject, if you ask the hotel to send you to a rug store or to get you a guide you will pay at LEAST 20% more for it than you would have otherwise. Concierges ESPECIALLY at the best hotels let alone guides have standing commission "agreements". Then again you must have an idea of whta value/price are otehrwise you will get screwed. Plain and simple.
The ere are old rugs/kilims around you just have to hunt for them but they may be pricey. As far as silk rugs are concerned, make sure that they are Turkish. There are a lot of Chinese silk rugs around sold as Turkish that are relatively worthless.
The FS was a most definately a prison, as a matter of fact the Midnight Express guy was held there for awhile. The Ciragan does have a great location, view, pool etc. BUT many of the rooms are NOT so spectacular. The palace rooms/suites are SPECTACULAR but there are very few of them and they are quite pricey.
DO not stay at the Conrad. I know countless people who have stayed there andno one is happy with it. The service is terrible there. The Swissotel has seen better days and is in bad need of a full makeover. Rumour has it that Swissotel's contract is over and they will not be renewed.
The new RC is quite nice, and is in Taksim (right near the IC, Hyatt, Divan, Hilton, Marmara, etc.). Of those I just listed the IC is probably best. That being said the Taksim area is not the "new" area as described earlier in the thread, Taksim and Beyoglu are quite interesting and historic as they were mostly built in the 1700-1800's by European "communities" and are quite historic in their own way. If you want new and bland and like a lot of other places go to 4. Levent or Maslak (Turkish Manhattan), hell go out to Atasehir or Bahcesehir, large 50,000 apartment cities on the outskirts of Istanbul).
BTW, for US customs items like handmade Turkish rugs are NOT TAXED. It should also be mentioned that be careful of antiques as any true antiques are NOT exportable from Turkey if they are of Turkish origin (but you can export antique rugs from other countries).
Staying in the Ayasofia area has its merits as its in the center of most of the "classic" attractions. That being said it is distant from everywhere else and quite empty at night. How can I put it, neither myself, nor my friends (Turkish or Foreign) would ever "hang" in the Sultanahmet area, its just too touristy and gets worse every year (although its still more "real" than anywhere else in Europe).
You could always stay at the "classic" Pera Palas hotel. It is where Agatha Christie wrote Murder on the ZOrient Express and for decades was the premier hotel in Istanbul.
Lastly (and never suggested on FT before) you could stay at the Bebek Hotel which is located literally on top of the water in Bebek, one of the most exclusive areas of Istanbul. The Bebek hotel bar (outside) is where the "important" people meet and the whole area is quite interesting. It is a small hotel with no super amenities but has a lot of cache locally.