First decide on the theme of your vacation, in June, weather in mountains will be pleasant, you may cover Dalhousie & Khajjiar (nearby), McLeodgunj and Dharamshala (like twin cities) in 4 to 5 days. You need to check flight connections from Jaipur to Jammu (to go to Dalhousie by cab) and from Amritsar to Jaipur (come to Amritsar from Dharamshala and fly to Jaipur after visiting Golden Temple).