Shot this video on my visit to Sikkim. Rangka or Lingdum monastery near Gangtok is a pleasant visit. Sunset from the monastery terrace offers good shots with the Himalayan backdrop.
To get there: Rent a car from your hotel, the easiest. The local drivers are friendly and will help you around.
Shopping: The monastery area has a couple of stores and a restaurant. The shops sell souvenirs at reasonable price.
Food: Sikkim is dominated by restaurants selling Momos and Wai Wai noodles, both of which are made from corn flour. Make sure you get your fiber from salads or the Sikkim trip can be painful.