North Sikkim is sold in two-night packets from Gangtok. Gangtok → Lachung → Yumthang → Gangtok, three days. You will see Yumthang for forty minutes. You will shiver, take three photographs, return.
Slow down
Spend two nights in Lachung. Spend two nights in Lachen. Do each morning slowly. The peaks do not move.
Stay in a homestay, not a hotel
Lachung and Lachen have about forty homestays each, run by Bhutia-Lepcha families. The breakfast is made by the grandmother. You drink your second cup of butter tea while the family goat watches you from the courtyard.
The difference between a hotel room in North Sikkim and a homestay is the difference between watching a documentary and being invited into one.
Add Gurudongmar
From Lachen, do the pre-dawn drive to Gurudongmar Lake. 5,430m. India's highest drivable lake. Sacred to three religions. Blue in a way you will not see again at any altitude you are likely to go to.
Skip a day to earn a homestay night
Skip Zero Point if you must — it is crowded, especially in April. But do not skip the evening in Lachung with a wood-stove, a bowl of thukpa, and the river going past below your window.
That is North Sikkim.
