Garanti, Akbank (I think) and Finans all have English language online banking; there may also be others. We use Garanti and Finans, and from a usability aspect, Finans wins hands down. Fee's and charges are reasonable, we negotiated fixed charges for receiving funds which helps. Quite a few staff in the Fethiye Finans speak English; the girl who deals with expat accounts, Ayse, has a good reputation for being straightforward and helpful.
JF