I didn't go out GLBT style much since I flew in on Sunday and left on Thursday or Friday, but I really loved these restaurants:

Mikla - Great food, awesome view.

Leb-i Derya - Great food, really nice view, Seemed to be a good place for cocktails before dinner too, but we didn't make it back

Kosebasi - I think this is right near your hotel, so great if you're not in the mood to go far afield - great Turkish food, excellent service.

As for tourism, we did the standard set - Hagia, Blue Mosque, Reina Sofya, Ferry up the Bosporous, some Art galleries and history museums. Really great, but nothing off the beaten path.

Enjoy!
John