How to get to Yumthang Valley from New Delhi?
Air: The closest airport to Sikkim is Bagdogra, West Bengal. Hence, you can take any of the several flights from Delhi-Bagdogra that are scheduled throughout the day. After reaching Bagdogra you can hail pre-paid or shared cabs to Gangtok which is about a 124km from Bagdogra, ie. almost 4 hours away.
Rail: The nearest railway station to Gangtok is New Jalpaiguri, Siliguri in West Bengal, which is about 150km from Gangtok. The train will take you to NJP in 21 hours from New Delhi. After this, you can take a private/government bus from the main bus station to Gangtok, which will take you around 6 hours.
Road: It is convenient to take the road to Gangtok, only if one is living in the north-east or West Bengal.