Mysuru

Built by the royal family of Wadiyar, Mysuru Palace could easily beat any other palaces in India for the beauty and scale (if you exclude Rajasthan). During their rule, the Wadiyars also built Krishnarajasagara Dam, aka Brindavan Gardens, which is a wonder on its own. Construction of this dam formed islets which ended up creating Ranganathittu Bird Sanctuary. Salim Ali was a significant force behind formalizing it. Both dam and sanctuary are situated in the outskirts of Mysuru, which you can visit on the way to Bengaluru. One highly recommend place is Chamundi Hill; you should visit it during sunset as the whole Mysuru bathes in the twilight.

Mysuru Palace
The court in Mysuru Palace
Brindavan Gardens aka Krishnarajasagara Dam
Sunset from Krishnarajasagara Dam 
Ranganathittu Bird Sanctuary
Sunset from Chamundi hills