Zurich is not so far away from Stuttgart, therefore we have been there quite often.
Zurich is a great city! You can walk though the historic town or enjoy a boat trip on the Lake Zurich. When you walk up the Uetliberg you have a great panorama. When the weather is nice you can see the mountains!
And if you do like climbing Zurich also has great climbing halls 🙂 To relax you can go to the Thermalbad where you can enjoy hot water and a great view from the roof of an old brewery over the city!