Is safe parking garages readily available in Zurich, Switzerland?

Safe and readily available, yes. Cheap, not a chance.
There are signs around town giving directions to the different garages, and how many places are available in each. The garages are well-lit, although unattended (you pay by machine). I've never heard of anyone being afraid of them.

Contact a guy named cu8sfan at chessgames.com. He lives in Z眉rich, and he will be able to answer this for you.

Click on Bahnhof for central Zurich parking, which will be expensive:
http://www.pls-zh.ch/index.htm

What you mean by "safe"? Compared with most other countries, any parking garage is safe (enough), also the public ones. There is practically no crime in or theft out of a garage.

If you look for a long-term garage at a payable rate, the Hotel Intercontinental (Badenerstr. 420) has some offers in their own garage, which is also accessible for public.