The airport is around 15 Kms from the heart of the city, you'll get Ola and prepaid taxi services. Once you reach your hotel, depending on the time, plan the rest of your day. I reached Madurai around 5 pm, so I planned to cover the famous Meenakshi Amman Temple. The architecture is outstanding, do not forget to buy a ticket, which costs around Rs.100, otherwise you'll be in the line forever. Enter from the South Gate. Guides are also available and will charge you around 300-500. For dinner I went to Murugan Idli Shop, the mini onion uttapam and paneer dosai are amazing, must try, 5 different types of chutney are served. This diner is located near Pothys, South gate. After your dinner don't forget to try the local milkshake which goes by the name "Jigarthanda", it's made of honey and almond, there are many shops serving this drink, but the original one is near the East gate of the temple. To end the day you can stroll around the market, probably buy silk clothings.