Hotel near Zurich airport?

I don't know of hotels near the airport, but staying in downtown Zurich is so easy, there is no need to stay by the airport. We stayed at Hotel Arletts within 5 minutes walk from the train station. It was approximately 15 minutes by train to the airport and the train deposits you right in the airport. I don't remember the exact cost but am pretty certain it was under $200.
The hotel was nothing great, but it was clean and the location was very convenient. We were able to walk through downtown Zurich the day before our flight and still be close enough to the airport to make a morning flight with no problem.

Sorry - the hotel was Arlette - not Arletts.

Susan , you don't say when you will be there . Zurich is a business oriented city and weekend rates tend to be lower than during the week . Have a look at the Novotel Glattpark in Zurich . Four star , part of Accor hotels . Convenient location with city tram in front of the hotel , 5 minutes to the airport , 15-20 minutes to Hauptbahnhof . Prices about $125 USD on weekends .

Thanks all! This will be a Monday night before our flight early Tuesday morning Jue 2013!