If you choose to stay in hotel then you cannot much nearer than WOW Istanbul Airport (4star)
The price varies and you are better to try Tavel republic / Hotwire for booking.
The free shuttle leaves from outside the terminal.
If you book the hotel will email timetable if you ask.
Alternatively, it is only 1 Metro stop away. The Metro gets you into centre if you have the time.
The Metro is reached directly from airport.
And the taxi fare would not be extortionate either.
The journey is no more than 5 minutes.
The same applies for return to airport.
Breakfast is fine.
Buying meals and drink in the hotel is extortionate. There is a Carrefour a few minutes walk from hotel.
Big plus for the hotel is the proximity to airport.
There is a 5 star sister hotel next door.