So, while you're leaving Sikkim, I'd recommend you to visit kalimpong and before kalimpong, do visit taare bhir.
Since, just like Gangtok, kalimpong isn't more than a day's visit, you must head out to Darjeeling for the night. The valley looks beautiful at night. Oh, do visit "Glenary's" for breakfast, I have shared some delish pictures from the day, pictures from the resort's swimming pool and of course a picture at tarey bhir.
Tip: if your group is of adults of not more than 4, better get a cycle. It'd be fun and adventurous.