If you have more time, consider visiting the Sri Aurobindo Ashram that is known for its spiritual significance. You could also explore the French Quarter that has numerous cafes, art galleries, and boutique stores to discover.
If you have less time, you can skip the Botanical Garden or the Basilica of the Sacred Heart of Jesus. As an alternative, you can explore the Maison Perumal Hotel that has a beautiful courtyard and a rooftop bar with a great view.