Hi Chinmayee, You can explore Gangtok, Rumtek, Nathula Pass, Tsomgo Lake, Mangan etc over a span of 3 days. This is one part of Sikkim. Otherwise, you can also explore Pelling, Ravangla, Yuksom & Gangtok - this is another part. If you're going in winters, then the roads in the north would be closed, but otherwise Gangtok, Lachung, Lachen can also be done :)
Hey Chinmayee! Gangtok; Tsmogo; Nathula; Lachen;Lachung; Chunthang; Thangu; Zero Point; Yumthang; Gurudongmar. there are various places you can explore I suggest you to best three day could be Gangtok via Lachung Yumthang next day Lachen and to Gurudogmar lake via Thangu valley.Can also visit Zero point from Yumthang and Kala pather from Gurudongmar. If you are traveling in a group or individual take the package and you will need permission prior carry photographs travel in group in case to spilt expenses because any how only heavy vehicle is allowed on this route. You must book with agent before reaching Gangtok. feel free to ask! Happy Travel!