It depends what kind of yogurt you're looking for. Nearly every bakkal (small market) or grocery store will have yogurt far superior to anything in the states. If you are looking for standout yogurt, try Kanlıca yogurt. It's made of a mixture of sheep and cow's milk and is far thicker than most. It's made in a small village up the bosphorus towards the Black sea.
You can find it at specialty stores (look in Cihangir, the upscale neighborhood next to Taksim), or take a bosphorus cruise and head to the source.
Big fan of sakipaga yogurts and they're relatively easier to find: at Migros, Migros Jet, Macro etc. Not organic but without preservatives. You should look for yogurts that say "katkısız"