It will be pretty cold in December... So it's better to take plenty of warm clothes .... Places that you can cover within 3 days in Shillong are -
1. Elephant falls
2. Ward's lake
3. Polo ground
4. Police Bazaar
5. Shillong view point
6. Don bosco museum 7. Lady Hydari Park
December would be perfact to visit in Shillong though weather will be quite chilled but for that u can manage and regarding places,i would suggest u to please visit Laitlum,its enchanting view will leave u speechless and other than that u can visit Dawki,Krangsuri fall,Cheerapunji,Golf Link and so on.
If u quite interested in culture and then u must visit Don Bosco Cultural Museum.