The basic difference is that quiet can mean little or no noise, but silent means ZERO noise. If you describe somebody as quiet, it means that person doesn't talk very much. People can also talk quietly (with a very low volume) but itís impossible to talk silently!
This interesting abode is situated within the town of Goreme, Turkey which is famous for its unusual rock formations. Apart from the natural beauty of the region it could be worth the trip just to be able to say you slept in a fairy chimney.