There's so much to do in Sikkim, Tsongmo Lake, Yumthang Valley, Zero point and more.
You can find everything you need to plan a trip, find stays and also places to visit here - https://www.tripoto.com/sikkim
Happy traveling :)
Two days would be enough to explore Gangtok. On the way to Gangtok or while returning to Siliguri, you can try River rafting in Teesta River. Tsomgo Lake will take around a day. Nathula Pass and Zero Point can be covered in the rest of the days.