You should definitely check out Sensus Wine, which is located right next to the Galata Tower. They carry only Turkish wines. I guess they have more than 500 kinds in store. It's also a cheese boutique, where you can have a bottle/glass served while you enjoy different kind of cheese selection they offer. I recently bought a cab (Buyulubag - 2007) and it was probably the best I've ever had. And, it was around 35TL, which is not a lot when you consider Napa prices for the same quality.
This place would also be a great spot for a date. Location
Another new wine bar is Solera on Yeni Carsi, just off Istiklal by Galatasaray high school. The wine prices are very reasonable (starting at 8 TL/glass), and even cheaper for takeaway. I just got a great bottle of a Cappadocia wine for 16.50 TL! The food is also surprisingly good (try the kofte plate) and it's a cozy spot.