Our experience with NH Hotel Geneva Airport started in the airport, when we were waiting for the shuttle to the hotel for almost an hour, whereas the shuttles to the rival hotels were much more frequent. We were surprised that, officially, the shuttles go each 20 minutes. On the way back to the airport next morning, it was the same: the shuttle did not come in due time, I went to the reception to complain, the girl said: next shuttle in 20 minutes, at 9:50. I replied that there had been no shuttle at 9:30. She was not surprised and eventually called the driver. The driver (an unpleasant old guy) promised to come in 5 minutes, but came in 10, opened the passenger door allowing us to enter, we put the luggage into the trunk of the car, but he... left us alone in the shuttle. We tried to stop him, and he said that he would depart in 2 minutes, but this did not happen. We eventually departed almost at 9:50, with a 20 minutes delay.
The receptionists are not effective, they were five(!) at the desk when we arrived - and only one customer - but still we had to wait. The one who ultimately served us wrote a wrong date in the free transportation ticket.
The window lock in the room was broken, it was not possible to close the window, but on the other hand it was the only way to get fresh air, since the air conditioning was very poor. However, very early in the morning we were woken by the noisy plane traffic from the airport, and it was apparently impossible to make it weaker by closing the window.
The hotel was not cheap, but breakfast was not included in our booking.
To conclude: even with early departure, I would recommend to look for cheaper and better options in Geneva for you can quickly get to the airport by train using the free transportation ticket provided by every hotel.
The Alpine park behind the hotel is nothing special but nice for a walk in the morning.
It is not easy to find the way to the Meyrin train station (maybe the fastest way to get to the downtown Geneva) and back to the hotel, but we managed to do it, however, there are also trams and buses in the area.