If you are alone and you have the ability to travel in a sharing option then for two days in sikkim you need minimum 9000/-...
there are so many places in sikkim .. i would like to give the basic plan which most of the travelers have been chosen.
njp/bagdogra to Gangtok via rongpo( don't miss to buy zong, a local wine product and trust me it was wow)
stay in gangtok
next day sight seeing in seven places near Gangtok by taking cars
stay in gangtok ( dont forget to walk around in the mg marg at the evening)
last day book a car or go with sharing facilities to changu and new baba Mandir. you can't reach upto nathula, the Indo china border due to heavy snowfalls at that time.
take a ropeway ride in changu
then come back to Gangtok and night stay there.
next day get ready for taking train or flight. don't be late as there is a hige traffic problem in the sebok road.