Okay, in that case you should take a flight from Chennai to Bagdogra. From Bagdogra, you get a taxi to Bhutan. Lot of people also hire bikes from Bagdogra and do a road trip but given it`s cold now, I wouldn`t recommend it.
Hi, You can take a flight to Paro Bhutan. And then make a plan which places you want to visit.
I am listing some of the places which you can visit:
Jigme Dorji National Park Happy Travelling!