Hi . ..apoorva...... plenty of options you have in your neighboring states like in tamilnadu, kerela and karnataka itself. some option you can consider like. 1 munnar in kerela 2 kodaikanal in tamilnadu 3 Connor in tamilnadu 4 waynad in kerela 5 araku velly in tamilnadu 6 Chikmaglur in kerela
7 idukki in kerela
May month is called as scorching month of South India, where cool places invite a traveller to enjoy and make memories in south India. Will share a tripoto link written by a traveller pertaining to their travel to south India see if it is suitable for your travel. https://www.tripoto.com/india/trips/hill-stations-in-south-india Here are some spots to explore more in south India
Kudremukh
Valparai
Chikmagalur Kolli hills
Meghamalai
Araku valley Lambasinghi
Wayanad
Asthamudi
Munnar
Kumarakom
Paniyeli poru
Coonoor
Horsley hills
Nandi Hills
Yercaud
Yelagiri Topslip
Kodaikanal
Try Kodaikanal for a 2-3 nights visit, try by the 2nd half of may to experience some summer rains as well, there are a lots of places to explore in kodai!