Elisa B.
Yelp
Lindenhof is a square nestled in the heart of the old town, but located high enough that you can enjoy a great view of the Limmat, a section of the Limmatquai and old town, the University up on the hill right across, and the Grossmünster towers on the right.
At the same time, it is a surprisingly peaceful location, so it's a great place to stop for a snack (which you must bring along, there are no restaurants or kiosks here), read a book, have a chat with a friend, etc.
A lot of people like to sit on the outer wall and look down at the river and people-watch, but I personally don't recommend it because you are quite high up!