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Since you have 11 days of travel where two days goes off in travel up and down, here are some places to cover in 9 days. You can reach Bagdogra or Gangtok from mumbai by air or train. You could start with Gurudongmar lake from Gangtok by bus or cab for its 6 hours away. Here are some more places to explore in north Sikkim
Lachen
Zero point
Seven sisters falls
Thangu valley
Chopta valley
Mangan Thangu Each of these places are three hours distance from one another. Not all only a few rest places are more than 6 hours 7 hours distance. You could plan two days in a spot and cover 5 spots or plan travel to each place a day and try covering more spots. Upto you.
https://www.tripoto.com/sikkim/trips/best-homestays-in-sikkim https://www.tripoto.com/sikkim/trips/homestays-in-sikkim
UpvoteCommentI will share a few tripoto links regarding stay in the main article, kindly check to see if it helps you in your travel.