The people of Tamil Nadu consider providing food to others a service to humanity. Thus the service in the state capital, Chennai, is first-rate. Treat your senses to some of the richest South Indian flavours in traditional dishes like sambar, rasam, fish curry or kootu. And don't forget to have a cup of full-bodied Tamil coffee, enhanced with chicory—no visit is complete without it.

Known as both the "Garden City" and "The Silicon Valley of India," Bangalore (officially "Bengaluru") is a techie’s paradise, boasting the highest concentration of IT companies in the country. When you’re done geeking out, there are plenty of gardens, museums, natural features, palaces and temples to fill your dance card. Visit Vidhana Soudha, Cubbon Park and the Ulsoor Lake of Bangalore, well known for its beautiful locales and boating facilities. Bangalore is also a major centre of Indian classical music and dance, and of vivid, cutting-edge nightlife.

Thrissur is regarded as the cultural capital of Kerala, a beautiful coastal region of southwest India with a history deeply rooted in the spice trade. For an exercise in absolute serenity, schedule an overnight houseboat tour of the local backwaters. If you’re lucky enough to visit during the temple festival of Pooram, you’ll experience lively music performances, fireworks, shadow puppet shows and processionals of beautifully adorned elephants.

Srinigar is a modern waterworld, dominated by Dal Lake and its twisting waterways, tree-lined Nagin Lake, and the Jhelum River. Engulf yourself in local culture by embracing your sea legs and renting one of the wooden boats called shikaras for a daytime or twilight cruise. On land, stroll through the terraced hillsides of the 400-year-old Mughal Gardens, created by Emperor Jehangir for his wife, and shop for indigenous crafts like hand-woven silks and embroidered shawls.