So 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 you can go by road, air, or train as well.
By road. Bhutan can be entered form the border of West Bengal namely Jaigoan. A freely accessible gate bifurcates Indian side of Jai Goan and Bhutanese side of Phunsoling.
The neatest airport is Bagdogra, the journey from Bagdogra to Jaigoan has to be done via road , takes approximately three hours.
The nearest railway station is Hashimara which is approximately half and hour from Phunsoling, or otherwise from N.J.P railway station the distance is approximately three hours.
Bhutan can also be entered via road from Gelephu and Samdrup but these routes though very scenic take a long time to reach Thimpu(10 hours and 3 days approx) so Phunsoling one is much preferred. By Air. You can enter from Paro airport, There are flights to Bangkok, Delhi, Kolkata, Bagdogra, Bodh Gaya, Dhaka, Kathmandu, Guwahati, Singapore and Mumbai. There may not be daily flights from each of the above destinations , but the permit obtaining process is comparatively hassle free if you enter Bhutan via Paro airport.
From Bangalore you can take a flight to Bagdogra Airport and then reach to Bhutan or you can take a direct train to siliguri or new jalpaiguri and then to Bhutan from there by Road
you can even take a flight to kolkata and get train from kolkata to new jalpaiguri or siliguri and then by road to Bhutan if you want to save up some money..