The Lindenhofplatz is the oldest part of Zurich at an elevated position in the old town.
When walking from the main railway station, it will be above the right bank of the Limmat river. You need to take an easy walk up to an elevated plateau where's a park with benches overlooking the entire town. Beneath it are Roman ruins, the oldest part of the city, but they're not in great shape and not that interesting.
Close by is the St. Peter's Church.