Slim pickings indeed at that budget.

Here are a few, however.

When it says "Double from", they mean FROM. That low price is in the dead of low season or when the hotel is likely to be half empty. The upper end of the range listed in the "room rates" is the more likely price. Best of luck.

http://www.eurocheapo.com/zurich/hoods/old-town.html

I would rather spend that nite in Luzern---the train runs direct from the airport and is only about 1:20. I like hotel Des Alpes--a 5 minute walk from the station.

In June, for example you are going to be paying more than $200/night at Des Alpes but since we do not KNOW your dates it is hard to answer your question

Here is a website that lists Swiss budget hotels and there are four or five available IN Zurich if you are interested:

www.rooms.ch

That is an extremely low budget for Zurich - since Swtiz is the most expesnive country in europe. Must you there? Why not move on to Italy right away where prices are more moderate?

http://www.st-josef.ch/

Try the hotel Fly Away in Kloten, a 5 min free shuttle away from the Zurich Airport. A random night in June (20th) prices at $201 for a double.

Its comparable to a Marriott Courtyard (sans the carpet) but only 40 something rooms.

http://www.tripadvisor.com/Hotel_Review-g198838-d266699-Reviews-Fly_Away-Kloten.html

For much less than $200 check out a Hostel.

Would second the Hotel Des Alps in Luzern. Older and a very small lift but rooms have been redone recently and its a great location just across the bridge from the train station.