Former capital of the Wodeyar kingdom, about 145 km south-west. The Bengaluru–Mysuru expressway and frequent trains make it an easy day trip. Highlights are the Mysore Palace (illuminated on Sunday evenings and during Dasara), Chamundi Hill, Devaraja Market and the Brindavan Gardens at the KRS dam. Combine it with Srirangapatna on the way.
Further reading: Mysore on Wikipedia.