A hill fort about 60 km north of the city, near the airport. Tipu Sultan used it as a summer retreat, and the clifftop "Tipu's Drop" is named after him. Locals drive up before dawn to watch the sunrise above the clouds. The ancient Bhoga Nandeeshwara temple at the foot of the hills is a must. Weekend entry is often regulated, so check before you go.
Further reading: Nandi Hills, India on Wikipedia.