When visiting a city for a short time and especially for the 1st time in your life, without yet knowing when (or if) if you will ever be back … just walk! You will be tempted to use a cab or public transportation or rent a car to get the most out of the city but please don’t, just let your feet take you to secret places.
A smart tip (better before getting there) is to have chosen the most iconic sights (no more than 2-3) you really wish to visit. Get this on your schedule – no further agenda please, so not waste time and energy in planning – and start wandering around. This way, not only you will do sightseeing but you will get the real feeling of the city (especially if it is a working day of the week), you will maximize and you will get the most out of your trip. You will have pictures to share and most importantly experiences to describe to your family and friends.
Just try to live for a while as locals do and hang around as tourists do.
P.S. If the sun is touching you, will be great! (photo of Zurich’s old city by the river)