Just tried the DT Avcilar. Very nice lobby, very nice rooms, very big breakfast buffet. My sleep was slightly disturbed by a lot of cracking noises in the ceiling (the building still seems to be settling).
The location is totally useless for the city (I booked it by intention to visit a factory nearby), but the best of Hilton's properties for the airport. That said I saw no indication of an airport shuttle, but didn't look out or ask for it.