Hey Shehreen
Destination Points of Himacal Pradesh, Uttarakhand or North East state will be better option if you are planning in the month of May - September.
Well inquire it on Google for bookings etc.
Before I suggest you the destinations that you should consider visiting in May-June, I am telling you the places that you should avoid if you already have them in your mind.
1. Kerala – Unless you love travelling in rains, avoid Kerala. Monsoons arrive pretty early in Kerala, and it can ruin your travel plans
2. Rajasthan – Rajasthan is extremely hot during summers and hence not ideal for tourists
These are some destinations that enjoy good weather during summers:
1. Himachal Pradesh – Manali, Tirthan, Jibhi, Parvati Valley, Spiti
2. Ladakh
3. Kashmir
While you may consider Northeast India also, be prepared for some rain.
Additionally these are some more destinations that you may consider:
https://www.tripoto.com/trip/best-places-to-visit-in-may-in-india
If you are looking for Indian destinations then I'm mentioning 5 of them down here:-
1. Kerala ( Munnar, Wayanad or Alleppey)
2. Jaipur or Udaipur
3. Amritsar
4. Agra
5. Leh-Ladakh