Why stay in Zurich? It's not very interesting. Geneva is pretty boring too. There's no need to join a tour, Switzerland is one of the easiest countries to travel in. For your plan, it's best if you get a swiss rail pass that allows unlimited travel on most trains, buses, and boats. There's a 6 day pass which would fit your schedule well. The Interlaken/Jungfrau region deserves more than a day, but make sure you go there on days with good weather.