Bangalore is comparatively nearest to reach Coorg. There are two routes, see which is suitable for you.
Via Mysore Madikeri highway - It takes 6 hours to reach Coorg. Another route is Nagarhole route which is 7 hours drive. You could cover Mysore for a day and stop by to visit Palace, zoo and Chamundi temple. From Mysore ooty is nearby popular for boating, peaks and gardens. Fruits, veggies are fresh along with homemade chocolates. Besides to cover you could stop by Nanjangud Shiva temple, Bandipur anyways you are visiting and Wayanad. Once we did a trip from Mysore to ooty, Wayanad and Coorg. It was 10 days trip.