If your flight is late in the evening then you may be better off at a hotel that allows 24 hr check-in/check-out meaning your checkout time is 24 hours from when you check in rather than the customary 11AM or 12 noon. For morning or early afternoon departures I usually stay near the airport at the Trident, Raddison or Le Meridian or in town at the Marriott Courtyard Inn and for evening departures I stay at the
Harrisons Hotel in Nungambakkam that is a 24 hour check-in/check-out hotel. The Harrisons Hotel is only about 15 minutes by taxi from central Station.
There are taxis available outside the hotel that you can engage to take you to the airport from the hotel.