6 weeks in India
The cheapest way to travel is Aeroflot. Moscow - New Dehli is ok. Oslo - Moscow, well they still use old Tupolevs that looks pretty run down. In the 12.50 AM April 16. 1999 there was no air coming in, and the heating system "on" or "off". That the plane was filled with drunken Norwegian teachers did not help.
Arrival in New Dehli is at dawn - pitch dark when landing, and morning light when outside.
I don't like New Dehli, but that might be my fault. I find it noisy, polluted, hot, and all the time there are someone trying to persuade you to travel in another direction, way, get another hotel ... even at the free bus between the two terminals (international an domestic) there may be someone trying to get some tips by "fixing" the driver to take you on. It took a whole day to find the Ashoka Rock edict. (Pictures, video but the text is in Norwegian only.)
One word of advice: Do NOT eat biryani unless it is cooked for an hour or so. I got a food poisening lasting 44 hours in fever.
So I headed for the mountains in Sikkim.
If you want to see Indian efficiency at its best, fly Jet Air. They are great.
The normal way to Sikkim is by Darjeeling. You need a permit to enter Sikkim, so get down to the District Magistrate, fill in a form, get up to the Foreign Registration office to get this form registered, and then down to the District Magistrate to get the actual permit. This permit is for two weeks, but it is no problem getting it prolonged for a month when you are in Gangtok.
This can be made in one day, but though Darjeeling is filled with tourists (all from Calcutta it seems ...), it is a nice place, so if you have the time give it a week or so.
Nice and reasonable hotel - the Dekeling is clean, the room I got was rather spacious and if the sky had cleared up, the view of the Kanchenjunga would be great, and the Tibetan family running the hotel is very friendly. And, the stairs up to the hotel get you a lot of exercise!