There are thermal baths all over the place (Baden isn't that far), but there is also a wonderful spa in the Hotel Dolder Grand (its one of the most luxurious hotels in Switzerland, and you get a really fantastic view from there), you can easily just go there for the day. Otherwise I'd of course walk down Bahnhofstrasse (it goes from the train station to the lake) and is a great place to go shopping. For a nice view I think a great place is the Polyterasse (go up to the university, just take the polybahn from Central and you are there). Of course you will want to see the old center of the city (Lindenhof, Limmatquai, the many churches). Prices in Zurich are about the same as in London. Zurich is known for being one of the city with the best quality of life ( I can confirm they are probably right). If you are looking for a hotel I would say that the baur au lac, the widder, the schweizerhof are really nice places to stay, but of course Zurich is full of hotels.
If anyone is planing a longer trip I'd say that places to go would be zurich, lucerne, vals (there are great thermal baths there, and they were made by a very famous swiss architect), geneva and the south (lugano, locarno). Switerland is quite small so its not hard to see a lot. a logical itinerary would be to start in geneva (see maybe some of the countryside, its very beautiful and they produce very good wine), bern (its not a must but quite a nice place), zurich, lucerne, (take the train from here you get to see some wonderful scenery), bellinzona, lugano. (there is an airport in lugano agno if you want to fly back). Switzerland is full of mountains so its not hard to pick...
it also works in a reversed order, or how ever you like, Switzerland is so small...
Hope you all have fun!
if I'm not mistaken the state of Virginia is like 3 times Switzerland, that might give you an idea