Tamilnadu is best option for you in December. You can explore Chennai, Mahabalipuram, Pondicherry, Trichy, Thanjaur, Madurai, Rameswaram nd Kanyakumari.
I understand your preference is southern India, but I definitely have to recommend Spiti Valley. It's the best place to do solo trips. it's breathtakingly beautiful and you won't regret a moment you spend there. However, if you prefer Southern, visit Coimbatore and the hill stations around it like Ooty, Kodaikanal. There are places like Aadhi Mahashankar you can go and visit along with its aashram if you are looking to spend quality time at one place.
Pondicherry to enjoy the French vibes
the beautiful beaches of Kerala- Kovalam, Varkala, Poovar Island, even you can add Kanyakumari too.
Visakhapatnam, Araku
Rameshwaram
Hi Aniket. If you're interested in Historical, you could the Chettinad Region - based out of Kanadukathan (3 days), Thanjavur (1 day), Pondicherry (3 days). The temperatures are also ambient during December. Happy to elaborate if you need.