From Darjeeling it is possible to do the Singali La trek. The start point of the trek is a place called Mani Bhanjang on the West Bengal/Nepal border, about a 1 hour drive from Darjeeling.
From here the route follows the border up to Sandakphu and Phalut, the high point of the trek at 12000ft. There are fantastic views of Kanchenjunga, the worlds 3rd highest peak, and it is also possible to see Everest, 100 miles to the west. The full trek will take you to the finishing point of Rimbik by day 6. A shorter version will go via Sandakphu and get to Rimbik by day 3. From Rimbik it is a 2 hour drive to Karmi Farm…the perfect place to relax after your trek