Ah, That changes things dramatically. In that case, I'd suggest thinking about Winterthur or St. Gallen. Both of these cities have excellent connections to the Zürich airport. They also have excellent train connections to the Rheinfall, Schaffhausen, and the Bodensee. There are a lot of really cool little towns in this corner of Switzerland. Winterthur is pretty cool, as it's a very non-touristy live city. St. Gallen has a lot more going for it though. There's also a stand selling bratwursts at the train station that has some of the best in Switzerland.

As far as Liechtenstein. I really wouldn't bother with it unless I had a car. But if you have a car, go up to Triesenburg.