I was able to cover all the above places in half day, and I chose walking as my mode of transport. The places are near to each other so if you love walking then quit motor transport and choose walking, it saves a lot of time too from traffic and you will get the real street experience. People are so friendly so you'll never get lost. Since it was only a one day trip my focus was on the above places only, there are many more places to be seen in and around Madurai so accordingly plan.
Happy Travelling and Live to Travel :)