Heidelberg's Altstadt is the old town below the castle, threaded by the long pedestrian Hauptstrasse. The street runs from Bismarckplatz across the historic centre, with shops, cafes, university buildings, side lanes, and views up toward the castle.
It is not a single monument, but it is one of the main pleasures of Heidelberg. Walk it slowly, duck into the smaller streets, and use it as the spine for visiting the Old Bridge, the castle approaches, and the university quarter.