Barsey Rhododendron Sanctuary is located on the edge of Singalila Range in West Sikkim, but it is located on the border of West Bengal and is also close to Darjeeling. It is a quick short trek but one can for further into the interiors if one wants.
Pithoragarh is directly connected to Delhi with overnight buses from Anand Vihar ISBT (NOT Kashmere Gate ISBT). The nearest train stations to Pithoragarh are Haldwani-Kathgodam (Ranikhet Express from Delhi) and Tanakpur (No direct trains from Delhi). From Kathgodam you can get buses or shared cars via Almora to Pithoragarh (200 KMs) and from Tanakpur via Champawat to Pithoragarh (150 KMs).