I have seen other suggestions too on this thread Zurich weightlifting
They mention Davids Gym on that thread but I have never been there so cannot confirm what is there.
If you want to try out Ghetto Gym or to see if Angel can offer training at Balboa which has the rack etc then you can contact [email removed]. Ghetto Gym and Balboa are more class based but I am sure they would let you just go there and train outside of class times if you coordinate it with them. Rather than big chains like Holmes Place or Silhouette these are independent places run by trainers themselves.
Reebok Crossfit Club Zurich also has the concept of open gym where you can just go along and train by yourself if you are a member, or you can pay per session. And they have a lot of free weights etc. Their site is http://www.crossfitzuerich.ch