Königstuhl is the mountain that rises behind Heidelberg Castle, giving the city its green backdrop and one of its best viewpoints. You can reach it by funicular, by road, or by hiking up from the castle area if your legs are ready for a climb.
The summit is most satisfying on a clear day, when the Neckar valley, old town, and Rhine plain open below. It also connects to forest trails, making it a proper outdoor escape rather than just a lookout platform.