I'll agree with everyone else - what a fantastic place.
I'll never forget the sight of the Blue Mosque by night, the call to prayer, the noise, the people, the smells and how big and ornate everything is - got neck ache from looking skywards the whole of the time!
My top places:
Topkapi Palace - what a wonderful place this is - but you need to allow pretty much a whole day to see it all.
The Blue Mosque and Aya Sophia of course - wow, amazing!
A visit to the spice bazaar is a must and of course the Grand Bazaar.
Gulhane Park is lovely too, takes you from Sultanahmet right down to the sea.
It's definitely worth buying a decent guide book before you.
There's a small Kofte restaurant near Sultanahmet restaurant - well known for its meatballs - they've got to be the best in Istanbul! And just outside the Blue Mosque (Hippdrome square) there's a really good Turkish kitchen (restaurant) - great food and very reasonable.
Nightlife in Sultanahmet seemed to be pretty low key but that may have been due to the freezing temperatures in February! Boy it was cold!
Don't take sterling travellers cheques - I could only change mine in the banks and the queues were horrendous. They seem to prefer dollars or Euros.
It's a magical place but we warned - it'll leave you wanting to return.
Enjoy!!!
Mazz