I did a solo trip of Sikkim on April this year. You won't be able to cover the whole of sikkim in 10 days. however, a brief itinerary can be like this:
Day 1 : Reach gangtok via siliguri/bagdogra. Stay near MG road. Visit the MG road in the evening. Have your dinner at Taste of Tibet if you are a foodie.
Day 2: A one day trip to Tsomgo lake, Baba mandir and Nathula.
Day 3,4,5: A 3 day drip to north sikkim - Lachen, Kala pathar, Lachung, Gurudongmar lake.
Day 6: Take rest as you will be tired from all the journey.
Day 7: Local sightseeing of gangtok - Tashi view point, Hanuman Tok, Rumtek monastery, Lingdum monastery.
Day 8: Leave for Pelling via Namchi and Ravangala.
Day 9: A full day in Pelling - Visit Skywalk, Rabdantse ruins, yuksom and Kaecheopalri Lake.
Day 10: Return to siliguri/bagdogra.
The itinerary is flexible. You will get shared cabs everywhere except in pelling. For baba mandir, nathula and lachen/lachung, you'll require permit. In peak season there is waiting for 3-4 days. you can either walk directly at the Sikkim tourist office or you can ask your hotel/hostel manager and check if they can get it arranged. they charge 100-200 extra but it saves time.
alternatively you can cover old Silk route instead of namchi, ravangala and Pelling.
However I havent' covered the old silk route yet. For any other details you can message me anytime.
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