For the morning, visit the Kolar Gold Fields. One of the deepest gold mines in the world and a heritage site, it is a must-visit for those interested in history and geology. Have lunch at Hotel Udupi Grand and then head to the Someshwara Temple, a 14th-century temple with an impressive gopuram. End the day by watching the sunset at the Antaragange Caves, a network of caves that is a popular pilgrimage site.
Wake up early and head to Nandi Hills for a lovely sunrise view. Spend the morning wandering around the hill station and enjoying the fresh air. Have breakfast at the Nandi Hill Cafe, and then drive to the Bhoganandishwara Temple, a 9th-century temple complex that is a great example of the Dravidian style of architecture. End the day at the Lepakshi Handicrafts Emporium, where you can shop for local handicrafts.
Consider stopping by the Kotilingeshwara Temple, which has over 100 crore (1 billion) lingams, or visit the Avani Betta, which is believed to be the birthplace of the Hindu philosopher, Valmiki. Take a day trip to the Anthargange Trek, which is a popular trekking destination. To maximize your fun, consider renting a car for the duration of the trip to have the flexibility to explore more.