Bebek Hotel, on the Bosphorus. Bebek itself, the neighborhood, is pretty swank and the hotel/bar is also apparently a place to see and be seen (though it didn't strike me as particularly fancy). Cagatay says it's a place where married men like to bring their young mistresses. :)
I haven't been inside the fortress yet - apparently there's not all that much - but I remember it from, er, Ali's season of The Bachlorette, when she takes some of the guys there to compete for her affections through olive-oil wrestling. Yes, I'm completely serious.