If you want to experience the biting chillness now is the right time to visit. Summers are warm though not much hot making travel to Sikkim pleasantable. If you want to explore extensively without hurrying, 15 days is much needed.
The best time to visit Sikkim is in the month of April and May not so cold but if you like winters you should pay an visit in the month of december and January .If you want to witness summers then August and September should be you choice and make site you have Gurudongmarg in your list for sure best time to see this place is september .If you want to see frozen gurudong marg lake then january and feb is the best time .
i hope it helps.