Hey Somya! Sikkim is awesome travel destination to go for a solo trip. Highly influenced by vibrant Buddhist culture, do visit beautiful monasteries like Rumtek, Phensang, Dubdi, Lingdum and Sanga. Weather will be pleasant during September-October. More power to and have a safe trip!
If you have got time ,do visit the ZULUK,EAST SIKKIM to experience the 32 hairpin bends.Also,it is a hamlet close to Indo-China border located on the famous Old-Silk-Route.