The months you have mentioned is peak summer time in India. So based on weather let me suggest some hill stations. See if it is suitable for your travel plan. Nainital
Srinagar Meghalaya
Mahabaleshwar and Panchgani
Lonavala Munnar Asthamudi
Araku valley and lambasinghi
Ooty Coonoor Topslip
Coorg kudremukh Chikmagalur
Leh ladakh
Manali Shimla.
Wayanad in summer is hot. From June mid rains stop. Now Wayanad is a great place to visit. Coming to Srinagar yes till February snow fall closes many roads. You need to check and then travel safely.
Just go to renukaji in himachal and travel beyond like churdhar gattadhar etc and forget yourself you will find peace , tarditional pahadi culture , camping ,thrill, adventure all
If your month of visit is June, I would recommend Dzouku Valley in Nagaland. Home to some exotic flower only bloom at the valley during the month of June.