During June ,Gangtok is the prettiest.But it rains a lot so make sure you have an extra day or two to cover places that you might not be able to because of the rains.
No, I guess not. During this period the place will receive heavy rains which lasts till mid-late September. October onwards till Mid-December is a good time to visit SIKKIM. December to March - risk of road blockages, due to snowfall, in NORTH & EAST SIKKIM might spoil the fun. I am planning to visit SIKKIM for about 7 Days in the month of OCTOBER. Have made an itinerary, now sorting out travel plans as I am, as of now, a SOLO Traveller. If you have any other questions , please do let me know.