Ur question itself need correction, All Hill station have their own aura and charm. Until June you can explore northern part country like Himachal and UK.
June is the beginning of monsoon in many parts of India, that allows lot of fresh air, fresh greenery giving lush nature view. Here are a few to visit
Munnar - Asthamudi in Kerala
Coorg and Kudremukh in Karnataka Mahabaleshwar and Panchgani in Maharashtra Nainital and Panchgani in Uttarakhand Darjeeling and Pelling and Meghalaya in North east
Auli- Valley of flowers -Auli-Chopta -Kasol -Dalhousie-Mcleodganj are some more hill stations to explore in Himachal
Manali Shimla Gulmarg sonamarg and Pahalgam in Kashmir
I would suggest you to visit a hill station before June during April and May because there are chances of rain during June which might cause landslide. But if you want to visit a hill station I would suggest you to visit Kalimpong in West Bengal.