There are a whole bunch of 'cheap' hotels (ie. over £100 a night but less than £200) in Zurich, so spend some time on a website, like Trip Advisor.... Mostly city center, near the central station. Some can be noisy from the street, so try to check at reception. The rooms may be fairly small but will (or should be) clean and everything work.
Other than that, prepare your wallet for a real pounding......