In May, South India would be too hot as my experience. But still, I think places like kodaikanal, Alleppey, or Thekkady are quite good for summer. These places would also present the culture and traditions of South India.
May is a tricky month since it's summer. South India part will be hot. You can go to hill stations such as Munnar, idduki, vagamon, kodaikanal, kudremukh, ooty etc. Other places are(which I won't advise due to high temperature) are gokarna, pondicherry, Mangalore, udipi, hampi, malpe, Goa, Kochi etc.
I have travelled to Kerala during April and despite the heat in other places of South India, these places proved to be good as it had a variety of experiences. Munnar - hill station - 2 nights Allepey/Kumarakom - house boat stay - 1 night
Cherai beach - hotels and restaurants facing beach - 1 night Hope this helps.