Although Courtallam Falls is not in Madurai District, it is only about 160 km south of Madurai and it is worth a visit.  Only during the rainy season does it have sufficient water to attract tourists. It takes a little less than three hours (on a superb National Highway), with Srivilliputtur Temple (another must-see) almost exactly mid-way between Madurai and Kutralam.  The Main Falls and the Five Falls are a pleasure to check out.  If you must have a shower under the falls (separate for male and female tourists), ensure you take off your jewellery like earrings, chains, rings etc. as they may easily be lost under the full force of the falls! 
For kids Tiger falls is the best place to have a bath, as there are two small pools and a small stream. Passenger trains run from Madurai and express trains from Chennai.