Southern India Itinerary Advice

My friend and I are looking at visiting South India with the following locations in mind. Would love if anybody could add their 2 cents as to if there's anywhere in particular we are missing out on or if it's not worth visiting any of these places? Also some advice on how long to spend in each place would be amazing! No real budget or limitations but want to stay South. Planning on going in December.

Chennai

Pondicherry

Trichy

Madurai

Munnar

Kerala Backwaters

Varkala

Fly out of Coimbatore or Hampi