I would suggest you to stay at the city. If you prefer to use public transportation to/from the airport, I would suggest you to consider options near public transportation hubs that have direct bus service to the airport.

The hotels near the airport are either apartment hotels that are located in center of Arnavutköy, which is a local neighborhood that has no attraction for a visitor, or if you are speaking of the Park Inn by Odayeri, that is also in middle of nowhere.

There is literally nothing near the Kilyos area except for beaches and overpriced beach clubs + restaurants and there are not that much lodging options for a tourist over there.