Two destinations within easy reach of Mysore make compelling half-day or full-day excursions.
Srirangapatna (16 km north, about 30 minutes by road or local bus) is a fortified island town in the Cauvery River that served as the capital of Hyder Ali and Tipu Sultan. Tipu's summer palace (Daria Daulat Bagh), his mausoleum (Gumbaz), and the remains of the great fort wall are all here. The town is small enough to cover in a morning; combine it with a visit to the bird sanctuary at Ranganathittu just across the river, one of Karnataka's best waterbird sanctuaries.
Brindavan Gardens (19 km northwest, near the Krishnarajasagar Dam) are one of India's most elaborate formal gardens, laid out in terraces beneath the dam wall. The musical fountain shows run in the evenings and are cheerfully over the top — lit jets of water choreographed to Kannada film songs. Come late afternoon, walk the gardens before dusk, and stay for the fountain show after dark.