For travelling to SIKKIM you can either go by Shared Taxi (cost- 250-800) or booking (cost- 4k-6k).
After Reaching Gangtok if you have time you should manage to get permit for the restricted areas from the local tour companies .
Restricted areas- Nathula Pass, Tsomgo lake, Baba Mandir.
The local Attractions are-
1-Ganeshtok. 2-Gangtok ropeway
3-Hanumantok. 4-M.G. Road
5-Bakhtang falls. 6-Rumtek Monastary
7-Tashi view point. 8-Enchey Monastary
For getting the permit there is a waiting time of 1 day and you will be needing two passport photographs and your identity card. To compensate you can visit the above Local Attractions for which you can hire a cab - 1800 to 2500 (depending upon the season).
M.G.Road is must place to visit and have a lot of Showrooms , Restaurants , soveineir shops etc .