For the month of May, Ooty is the best place to visit. The climate is pleasant and ooty trip will take max 2-3 days to cover all its scenic beauty. a long weekend trip can work perfectly.
Hill stations are best summer spots. Manali Shimla Mcleodganj Kasol Nainital Mussoorie Auli valley of flowers Leh Ladakh Darjeeling Tawang Shillong Mahabaleshwar Panchgani Matheran Pachmarhi Ooty Kodaikanal Munnar Asthamudi Coorg Chikmagalur Kudremukh lambasinghi Arakuvalley are some places to enjoy cool air mist and lovely light fog.
Anywhere in Himachal, Uttarakhand, Kashmir, Ladakh should be good in summer to visit. If you want to explore South India, you can try Ooty, Munnar, Kodaikanal, etc.