After something to do when the weather is rainy? Take your time wandering around the interesting displays at Everest Museum. There's always an opportunity to learn a thing or two.
You're spoiled for sightseeing choice when in Darjeeling. Everest Museum is an ideal place to begin here, but there are plenty of other worthwhile spots to visit. Tiger Hill, Raj Bhavan, and Darjeeling Himalayan Railway are near the museum and will fill in your day nicely.