Minimum 03 days you need,
One for Nathula and Baba Harbhajan Singh Mandir, War Memorial, Tsogmo Lake
Second day for Namchi and Hanuman Tonk/Mandir
Mall road and local sight seeing
Sikkim is itself best. but for traveling, gangtok to North sikkim or silery gaon to silk route. also ravangla namchi and a lot more beautiful hamlets to explore.