Neckarwiese

Since Heidelberg is the warmest city in Germany.. the Neckar is definitely the biggest attraction here. Everyone goes here after class.. in between classes.. whenever they can! It's paradise on Earth, laying out in the sun surrounded by the most scenic landscape, grilling, playing sports etc.  

The Rhein and the Neckar are two separate rivers that extend throughout Germany and meet in Mannheim. "Rhein-Neckar Metropolitic Region" is also referred to as the Rhein-Neckar Triangle, located in South Western Germany, between Frankfurt/Rhine-Main region to the North and the Stuttgart Region to the South-East.
For students: rent a paddle boat/kayak and get a scenic tour of the Neckar

If you are willing to spend more: Go on a dinner cruise along the Neckar... getting the full experience of the old city.