Batasia loop, the derjelling mall, toy train ride from ghum station, Tiger hill, Peace pagoda, zoological perk... Do explore the food of Keventer and Glenary's, they are like heritage food restaurants of Derjelling. Best tym to visit Derjelling is throughout the year only avoid rainy season.
Hey Jason, The nearby places to visit nearby Mumbai in June would be :
1) Alibaug 2)Kalamb Beach (Nallasopara) You can even go on a trek. Kalsubai would be the best option. You can visit Karnala fort.
If you are residing in the north, Rhishikesh, Nainital, Jim Corbett, Shimla, Manali, Spiti, Leh, Sikkim.
Mid India - Rann of Kutch, Diu, Daman, Jaipur, Jaisalmer, Udaipur, Goa.
South India - Hampi, Ooty, Munnar, Varkala, Pondicherry.