For an unique history lesson, visit the crumbling remnants of Vijayanagar and imagine how it must have looked in its heyday.
You'll soon see why this Gangavathi once-important structure is visited by many travelers. If you're searching for other things to keep you busy, Anjanadri Hill, Virupaksha Temple, and Hanuman Temple are in the area as well. They won't take you very long to reach from Vijayanagar.