http://www.homegate.ch is the main website for apartments in Zurich. Have a browse and get an idea of how much things are.

Zurich is an expensive city. For apartments, demand far outnumers supply and so for anything less than CHF2000 (or even CHF2500), you will get plenty of competition for the same apartments. It's not unheard of that 200 people go see an apartment. You also have to weight that in as it's not just the "finding" a cheap place but it's also the getting.

Anywhere near the ETH (walking distance) is prime Zurich spot. Prices get less as you move further out but then you wouldn't be "near the ETH".

~ Nanda.