Darjeeling's pleasures are largely outdoor and unhurried. The light on the mountains, the smell of tea gardens, and the winding toy train are as much the point as any individual sight.
Tiger Hill is the classic sunrise excursion — a pre-dawn jeep ride to watch the light hit Kanchenjunga and, on clear days, glimpse Everest. Happy Valley Tea Estate is the easiest place to see how Darjeeling tea is made and to buy directly from the source. The Batasia Loop on the toy train line is a short drive or ride from town — the spiral of track in a garden setting, with Kanchenjunga visible on clear days, is one of the most photographed spots in the hills.
The town itself rewards slow walking: Chowrasta at dawn, the Padmaja Naidu Zoo for snow leopards and red pandas, the Himalayan Mountaineering Institute's Everest museum, and the Buddhist monasteries of Bhutia Busty and Ghoom.
A trip on the Darjeeling Himalayan Railway, even for a single section, is worth doing for the engineering alone. The steam service between Darjeeling and Ghoom is the most manageable.