Hi, COORG for me seems to be overrated. But if you still insist on going there, road trip is the best way. From Mangalore or Bangalore by road it should take you anywhere between 3-6 hours. Lot of eateries en-route and you will not get bored to drive on either routes.
Day-1 >> Drive to Coorg
>> Before checking in to the hotel, or if you reach early then post checkin, visit Abbey falls which is close to city
>> Visit the town and Madekiri Fort, Raja's tomb, Raja's seat (get good views from here for sunsets) and try to visit Bhramagiri Hills view point Day-2
>> Drive to Tala Kaveri and enjoy 360 degree views of mountains and wild life reserve
>> Relax at coorg hotel or resort Day-3 >> Drive to Bylakuppe (monastery) >> On the way stop over at Nisargdhama (just some kms before Bylakuppe)
>> Post monastery visit inquire with locals about Dubare Elephant camp, this is a diff exp as you can bathe the elephants and even play around Hope the above helps. Keeping in mind you are in Coorg to relax