Kanyakumari is connected by train to Trivandrum (85 km north), Chennai, and other major cities. The train journey from Chennai takes about 14 hours; from Trivandrum, around 1.5 hours. There is a small station in Kanyakumari itself, so arrivals don't require a transfer.
From Trivandrum, buses and shared taxis are also available and may be faster. From Chennai, flying to Trivandrum and taking a bus or train from there is the most practical approach. The nearest airport is at Trivandrum.