The best time to visit Gangtok is from late September to November and March to June. These autumn and spring-summer months experience a pleasant climate which is ideal for sightseeing. Between October and February, although the temperatures go below 0-degree Celcius, Gangtok takes on a surreal charm, opening a whole wide world of amazing activities. It is best to avoid a visit to this place during the monsoon months of July to early September since the heavy rainfall leads to landslides which may cause a lot of inconveniences.
According to me, the best time to visit Gangtok is in the month of May to June to escape the summer heat. furthermore to visit the other areas near Gangtok like peling, ravangla, lachen and lachung, any time other than monsoon is suitable though the winters are a bit chilly