Kovilpatti's food is southern Tamil home cooking: idli, dosa, sambar, rice meals served on plantain leaves at the small hotels near the bus stand. Most places open early for tiffin and close not long after dinner. Nothing fancy, but the staples are well done and very cheap.
Don't leave town without picking up a packet of kadalai mittai, the peanut brittle the town is famous for — see the shopping notes for where to find it.