If you're planning to explore North Sikkim, then you can start from Gangtok and cover Lachung, Lachen, Yumesamdong and Guru Dongmar (depending on when you plan to go!) Roads in higher altitude might not be open in the winters.
In case you plan to explore West Sikkim, you can go to Pelling, Yuksom, Darap village, Khecheopalri, Ravangla etc.
In East Sikkim, you can again start from Gangtok and explore Tsomgo Lake, Nathu La Pass, Rumtek Monastery, Tukla Valley, Nathang Valley, Jelep La, Hanuman Tok, Tashi View Point etc. Hope you have a great time exploring Sikkim :)
I highly recommend you to visit gangtok which is the capital town and namchi ,tsongo ,nathula pass, soreng,jorethang , silk route of India. .
this are the places you can visit and get satisfied of the beautiful nature
Sikkim indeed is a beautiful place to visit..but what places to visit choose upon which part of the place u r looking forward to visit..like if you are planning to visit east sikkim, then you should visit nathula pass which will definitely takes ur whole day..apart from that there are local guides over there who will help you cover small tourist points in a day itself..post that you should choose to explore other parts as well..since I only covered East Sikkim, I would definitely suggest you to visit other parts also..for pictures and places visit my profile..Thanks😊