I have been to a lot of solo strips from Chennai. You can start with Dakshina Chitra on ECR road in morning if you are interested in exploring culture. Then you can book a cab and go to Mahabalipuram from there. You can spend night in there in hotel nearby beach. Can feel calmness on beach in early morning. There are temples, caves and lighthouse to explore.
If you are looking for long duration trip then i will suggest you to go to Puducherry. You can spend 2N/3D there. Auroville, White Town, Promenade, Paradise beach are must visit places there.