Depends on the places you are going to visit and the hotels you are going to stay. We went for a 8N/9D trip to Sikkim and costed us around 20k excluding our flight cost. Must visit places:
Yumthang Valley and Zero Point
It depends from where you are travelling and there are a lot of places to travel in sikkim. The question is quite subjective. Assuming that you will be visiting gangtok and indulging in sight seeing for the other days the budget can be as follows : 1. You have to reach NJP station, from there you can book a cab or use share cabs which takes Rs 200-300 per head to take you to Gangtok. From there you have a book a local cab that will charge you Rs 200 per cab not head and will take you to your hotel room so if you are 4 people you fare will be Rs 50 per head.
2. Hotel room ranges from Rs . 700-1400 very good rooms with all amenities.
3. Food is quite reasonable. per meal may range from ₹60-₹300.
4. sight seeing price is Rs 700- Rs1100 by booking a local cab. He will take you to 7 points or 10 points depending in the price you pay. Per cab carries 4 people so money can be divided. I haven't included train fares coz I do not know fron where you will be arriving.