Thoothukudi, Tuticorin called by the Dutch, is known for its shipbuilding and the hinterland is used for salt winning.
More info about this town in between Rameswaram and Kanyakumarin you will find at Wikipedia
Indeed I was out of station, Madurai, for two days, going all the way by bike, got sunburned in my neck and my face.
The road from Rameswarem to Thoothukudi along the coast, was terrible, jumping through all the pits
I could even pass easily the cars that tried to avoid dammage. Finally in the evening, at sundown,
18:27, I arrived here to the vast salt winning plains near to this big town, exhausted from all the jumping.
If you think you can go quickly to have a look at the ships yard, forget it, you need a ticket and
it is open only on Sundays. The town itself is not that worthwhile to visit, so a nightstop on a
Saturday would be perfect if you are interested to see the shipsbuilding and then to go through to Kanyakumari.
The next day I went straight back for the Poongal Festival at Madurai, 140Km in two hours, the sun in my neck :)).