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.
All of Bhutan is worth seeing but these are a few places you should go
Paro taktsang
Punakha dzong
tashichho dzong
Kichu lhakang
national museum of Bhutan
chimi lhakang
And for stay check oyo, airbnb
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:
Paro
Thimphu
Trongsa
Samdrup Jongkar
Jigme Dorji National Park
Happy Travelling!
Hi, I have attached with this comment a destination guide for Bhutan, it contains all the details of places to visit, itineraries and trisps. You can check it out and plan your trip.