I am at the IST Hilton right now. Blue Mosque is worth the trip. You are given a disposable plastic bag to carry your shoes around. The Hagia Sophia Museum is more of a showcase of the architecture rather than artifacts. 25 TL for that tour. Weather is great, bring good walking shoes. Buy a transit pass "istanbulkart" from a kiosk (look for one advertising "AKBIL") see
http://www.turkeytravelplanner.com/g...anbulkart.html for info if you plan to get around a lot on mass transit (it's clean and quick). Best exchange rate I've seen is at the Grand Bazaar 179.2 for US.
The Hilton is near the Hyatt, Intercontinental and Ritz-Carlton (I can see the last two from my window), but all these hotels are in a business / residential district.
Have fun!
-outoftown