You are very central for everything there really. If you find your way down to the riverside at Eminonou you can easily walk to all of the main sights from there, you can walk across the Galata bridge and go up the tower, but just the walk across the bridge is an experience not to be missed. Even without the problems, Taksim square and Istiklal caddesi which is one of the main shopping streets don't do it for me, much too European, could be any shops anywhere, but a ferry up the Bosphorus (from Eminonou) is a great way to see the sights, (and dolphins swimming if you are lucky)
Karakoy fish market to the left as you go over the Galata bridge is a great place to eat with a fantastic buzz, and there are lots of restaurants under the bridge it's self. Just walking along the shore of the Bosphorus is an experience, watching the container ships going up and down. I could go on and on, I love it, and for me I don't really need to go in Mosque after Mosque, breathtaking though they are, because it has so much else to offer.
(ps, if the shoe shine man walks past you and drops a brush IGNORE IT!!!)