Here is what one can do to experience the best of Bengaluru and nearby areas for a day.
Morning Choices - Visit Nandi hills, Eat breakfast at Brahmins cafe, leave for Melukote and have breakfast at Bidadi - famous for "Tatte Idli"s
AfterNoon Choices - Visit Melukote visit temples and have Puliyogare (Famous flavored rice) for lunch, visit Somanthapura and enjoy the Hoysala architecture.
Evening Choices - Visit GaganaChukki, BharaChukki falls at Shivanasamudra, Have a boat ride at Sankey Tank at Malleshwaram or Madiwala lake near BTM Layout.
Night Choices - Visit one of the many Pubs near Indiranagar, Koramangala, and Brigade road or Visit chat street in V V Puram and enjoy the best street food of Bangalore
This is in addition to the places mentioned already by the author of the post.
Reach me if you need any further help.