Sam L, I didn't and I'm not sure where he is based. I really don't know at all.
Talula, that's a good amount of time to see the main sights, especially the ones clustered around Sultanahmet. I would recommend saying there to maximise your sightseeing!
I'd recommend getting started early. I just happened to be restless one night and got up quite early the next morning. I visited the Blue Mosque before the throngs of tourists had arrived. There were just a group of Koreans and a few people there for prayer. The first time I visited Istanbul actually, I went to the Blue Mosque about four or five times - at different times of the day. When I was there in October, I visited on a Sunday and there was a queue to get in (unless you were entering to pray) and it was packed inside. Much less enjoyable. Get started early.
I actually happened to be the first tourist to get into that Hagia Sophia that morning and even though I only had the place to myself (not counting a couple of security guards and one cat!) for a few moments, it was really, really amazing:
by keithmaguire 김채윤
, on Flickr
Anyway, you can see these two sights and the Hippodrome in no time. I would recommend the palace mosaic museum (unless you're into mosaics!) Topkapi Palace, the archaeological museum and Gulhane Park are just behind the Hagia Sophia and you can easily go from one to the other. As I said, think twice about Topkapi. Do some research and see if it's for you.
The Basilica Cistern is amazing and doesn't take long to see. It's just across the road from the entrance to the Hagia:
The Basilica Cistern
by keithmaguire 김채윤
, on Flickr
The Grand Bazaar and Istanbul University are only two stops west of Sultanahmet. The University isn't a must but it's not a bad idea if you're in the Grand Bazaar and wish to go to the Suleyamine (spelling!?) Mosque which is behind the university. There's also another major mosque near the east entrance of the bazaar which is quite nice. Can't remember the name of it but you could see it in Skyfall when they were running along the rough tops!
From the Suleyamine Mosque, Eminonu is walking distance. In Eminonu, you have the spice bazaar and the Yeni Cami (New Mosque) you can also take the tram back to Sultanahmet from here or walk across the Galata Bridge and up the hill to Galata Tower.
These, for me, would be the best sights in Istanbul and you could do all this in one full day, depending on how quickly you move and how long you stop for lunch etc. (this would definitely not include Topkapi though and you probably wouldn't have time for the Archaeological Museum either) You can visit the Blue Mosque quite late in the evening though, up to 9pm, I think. So, you could try to get to the things with shorter opening hours first.
Taksim isn't a nice square in my opinion but I hear they're doing it up. The MOMA is supposed to be quite good but they don't allow photography so I didn't go. The Ortakoy Mosque was still undergoing renovations while I was there in October (as it was in August 2011 - still haven't seen it!) You can see the Bosphorous Bridge from Dolmabahce Palace and as I mentioned it's really quite impressive. It's built to rival the greatest palaces in Europe and it does in terms of its interior in my opinion - no photography inside though (I've been to Versailles, Schonbrunn, Palacio Real and a couple of other palaces in Europe)
There's not a lot on the Asian side (you need to prearrange your visit to the Florence Nightingale museum, if you'd be interested in that - because it's located in the army barracks...which are a bit of a walk from the ferry) The Kiz Kulesi is nice but you can see it really well on some of the ferry crossings (esp from Besiktas to Kadikoy, I think but also pretty well from Eminonu to Kadikoy) Don't go out of your way though.
Eminonu is walking distance from Sultanahmet so if the tram's crowded, consider walking (it's pretty much a straight shot from the shopping street SE of the Yeni Cami - a straight shot to Gulhane Park anyway)
Try the durum kebabs, turkish delight and the ice cream if it's not too cold (it's not that great but the texture is interesting!) You might also want to try the kokorec!!