Kodaikanal rewards a couple of days rather than a single rushed day trip from Madurai. The main sights cluster around the lake and along the escarpment edge, with longer treks into the surrounding Palani Hills for those who want to go deeper.
The essential circuit covers Kodai Lake and a lap around it on foot or bicycle, Coaker's Walk along the escarpment edge, Pillar Rocks and nearby Green Valley Views, and the eerie Guna Caves in the shola forest. Add the Kodaikanal Solar Observatory if you have any interest in science — it is one of the hill station's less obvious but more rewarding visits.
For trekking, the surrounding Palani Hills offer routes ranging from the accessible trail to Dolphin's Nose to multi-day treks into the interior. The Shembaganur Museum of Natural History is worth an hour for its collection of local flora and fauna specimens.