I really could not fault the Greystone apartment. I stayed in apartment 2 which was on the first floor. You get a lot for you money, big apartment with tall ceilings, very tastefully (and newly) decorated and with a huge terrace which was nice but I hardly used it as I was out so much.
The host was very friendly and communicative. In terms of location it's within a stone's throw from the main shopping and nightlife of Taksim but enough out the way that it won't disturb your sleep. Restaurants, cash machines etc are all less than a five minute walk. It's barely a minute from the main road so you're not walking deep into a potentially dodgy neighbourhood. Do your google maps homework before you get there and it's easy enough to find.
I took the Havatas bus from Attaturk Airport which took around 50 mins and dropped me off in Taksim (Point hotel). From there it was about a 15/20 minute walk. If you come with suitcases however you'll want to get a cab as the pavements in Istanbul are not build for cases! Next time I'm in Istanbul I'll definitely be coming back here.