Shringeri Sharadamba Temple
The place whose soil has been blessed by the feet of the great Adi Shankaracharya. The temple is awesome and the surroundings serene. All visitors are served a midday meal in the temple premises.
To get there, it takes about 2 hours from Chikmagalur. Wear proper Indian clothes, and go with a healthy dose of respect towards age old ashram.
Like I said it's a large oyster, search for your own pearls.