We need a cheap ( I know; no such thing) hotel in Zurich prior to our flight the next morning. It doesn't have to be at the airport, but something very near a train stop that we can carry our luggage to.
We stayed at Easy Hotel not too far from the train station. Nice and clean, small room, somebody having a party in the street, but fine for one night.
The hotels near the airport are generally large and not cheap. We usually stay at the airport Hilton on our points. However, the hotels in the area around the Zurich main station (Zurich hbF) are much more reasonable. The Zurich main train station is about 12 minutes from the Zurich airport train station. Check out the Accor hotels (Motel 6 in the USA). I believe that there are a couple of IBIS hotels near the Zurich main train station. One of them is an IBIS Budget hotel.
spetry,
For hotels close to the Zürich train station, I'd highly recommend http://www.walhalla-hotel.ch/en/ as it's in an extremely convenient location! In fact there's an entrance to the underground Rail City only a short distance from the front door of the hotel (there's also a Burger King right at the bottom of the stairs, if that's of interest). If you'd rather enter the station from street level, that's also an easy walk (only about half a block).
If you have time for a bit of sightseeing on the day you arrive in Zürich, the small tour trolleys depart from the lot right across from the hotel entrance. The Trams also stop right in front of the hotel.