These gardens are extremely peaceful, and that is a great thing in Chennai!
The plants, especially the banyan trees, are breathtaking and if you walk a little bit off the beaten tracks you will end up finding wonderful surprises. The whole garden is very well maintained and yet wild enough for you to find plants and small animals you would not expect to see in a city. The whole place has a very special atmosphere and it is quite exciting to visit the gardens and imagine what life was like a few centuries ago.
There is also a library with a hidden treasure in it: you must absolutely ask to visit the "display room" and there you'll find unique books from all over the word, sometimes from the 15th century, on display: old Tibetan prayer books, Hindu mythology vedas engraved on palm leaves, illustrations donated by the ancient rulers of Java, books brought by European visitors... This is the opportunity to discover books you've never seen in your life.