Hi Viren, In June there will not be chilling cold & snow but yes at some places you might found cold weather. Also it depends what kind of place you want to visit.
Are you interested in trekking If yes i can give you few suggestion.
There will be rain and lots of fog. Moreover, due to collage and school vacation there will be lots of rush at all the major destination of Himachal.. Now there are two major areas. Manali region and Delhouise and Dharmshala region. Covering both the region in one trip could be very hectic.
Hi Viren You can try Waichin Magic Valley trek, Kheerganga trek, Grahan, Kareri lake trek, Nag tibba, Hampta Pass trek, Jalori pass trek and many more. But my personal favorite is Waichin Magic Valley.