This article is mainly ideas on how to spend a day or a few hours in Zürich. It may be that you are just in a short stop over or you still have time before you catch your flight in Zürich Airport.
Here are some places to check.
Zürich Hauptbahnhof Shopville.
This is the very first thing you can see when you step off from the train station. This is basically an upscale, mini-shopping hub inside the train station and can be found downstairs. Here you can see all kinds clothes shops, electronics, beauty shops even a health shop and coiffeur. There are of course lots of restaurants and food stands as well as supermarkets inside.
This is the shopping street that can be found when you exit the train station. There are lots of shopping streets but the Hauptbahnhofstrasse seems to be where the famous and big shops are and this way goes direct to the lake. This street looks really special and romantic because the trams pass along it and both sides of the streets have benches under some trees where you can sit down and enjoy the huzz and buzz around.
Of course no one leaves this city without seeing the lake. In summer, lots of people can be seen swimming here or doing some sun bathing. Swans are also an attraction here. Along the lake are restaurants and bars where you can enjoy a drink or a little snack. There are cruises than you can also take. For the timetable and types of cruises (there is quite a handful), this is the link.
Altstadt or Old Town.
This is just behind the Hauptbahnhofstrasse. Here you can see old buildings, museums, some old churches and of course, shops. If you want a feel of old europe, then a walk along the altstadt is an interesting experience.
This is an elevated area that was once a fortress facing a part of the Limmat river. From here you can see much of Zürich and the neighboring towns and villages. This is a very serene place and very beautiful.
There a lot more things to do in Zürich like visit the museums, the Zürich University, the old churches like the St. Peter and the Opera House. You can also take the lake cruises or book a tour of the city and its vicinity.
Realistically though, if you have just a few hours to spend, these places listed here are good enough already for you to have a feel of how the city is.