Reach New Jalpaiguri or Siliguri by train, which is well connected from throughout the country. Otherwise reach Bagdogra the nearest Airport.
Hire a car for Gangtok from NJP or Siliguri the fare range is INR 1500 - 1600.
The fare to Nathu La from Gangtok is also about INR 1600.
Many travel agents are available who will do the permits and other formalities for you
For accommodation in Gangtok you can choose from wide range of hotels. The cheapest available will be at INR 600/ day.
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