The Sirkeci District seems a bit overlooked. It lies between two tram stations, is near the Biggie Sights of Sultanahmet, is close to the Galata Bridge, and near ferry connections. We will be in Istanbul two weeks so jumping on the tram will part of our "daily commute." Our current choice for a hotel is Orient Express. And hello Agnes - The Guru of Istanbul.
We stayed in Sirkeci last spring at the Erboy Hotel. The Orient Express is a couple blocks away from the Erboy. We easily walked to all the sights and to the Golden Horn to take ferrys to the Asian side and to the Black Sea. We never did cross the Galata Bridge since there was so much to do in our 5 days there. We bought tram tickets but only used them once. You need to get on tripadvisor.com and Istanbul residents will give you lots of tips. Be sure and visit the McDonalds on your way to the ferrys, order a soft drink and sit upstairs for the best and cheapest view of the harbor!
Thanks for the great tips!
As far as views go, the best by far is off the Galata Tower (it's a very hilly climb to get to the tower itself though) - once you're at the top it's a 360 degree view of Istanbul..amazing!!! Another option is the cable car by the Eyup mosque/cemetery and Pierre Loti cafe (can get there via ferry - Eyup stop) - the mosque and cemetery are worth going to alone.