I had never been to Northeast India. Sikkim was always in the bucket list and there were huge expectations from this trip. Although there were some deviations, it was a fulfilling experience.
Sikkim - Overview
There are different parts of Sikkim and each part has to be covered at a stretch.
North Sikkim - You require a minimum of two-day-three-night to cover Lachen and Lachung. From Lachen, you can go to Gurudongmar lake and Kala while from Lachung, Yumthang valley, Zero Point and Katao can be covered.
East Sikkim - One day trip to Tsomgo(Changu) lake, Baba Mandir and Nathula pass.
West Sikkim - Requires around 2 days and 3 nights to cover Namchi and Pelling.
Gangtok - Places to visit are Banjhakri falls(you can also do paragliding here), Rumtek monastery, Ranka monastery, Tashi viewpoint(view of Mt. Kanchenjunga), botanical garden, and MG Marg road.
Note - You cannot travel in the night so the first day will be spent in reaching Gangtok. One more important thing to note is itinerary can only be prepared after arriving in Gangtok as some routes might be closed due to unfavorable weather conditions. So, I would advise you to book a hotel just for the first day and plan the rest later.