Most of North Sikkim will be closed at that time as North Sikkim is where the true beauty lies. Don't get disappointed. You can spend quality time in Meghalaya which is another natural marvel. Beautiful places to visit and experience. Plan Sikkim after March.
Both of them are good ... But with 30 years of experience in Tourism industry I will suggest you Gantok because you will get snowfall and North Sikkim will be all covered with snow.A perfect place to hangout with friends especially at that time .
Meghalaya is also a good idea but you won't be getting snowfall. It will be more of greenery and scenic beauty.
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In Gangtok there will be so much of snow falls and you can't be sure of visiting the desired places due to snowfall. In addition to it, weather fluctuates very frequently in snow fall regions whereasbin Shillong the weather will be pleasant but you can't experience so much of waterfall. The good thing is that you will get view of tropical hilly mountains for aesthetic pleasure.