hello Frank, I am familiar enough with these places (am travelling by motorbike in Sikkim at present). I f you have only 3 weeks, you'd be best to shelve Bangladesh (hopefully you can get there another time) as all types of travel in these countries will take much longer than you're used to (even air travel !). I'm surprised you wouldn't know this, having been several times in India. It's natural to travel north from Kolkata to Sikkim, you can get the permit easily in Siliguri (a pleasant city to stay for a night or two, despite what LP says, just go to the Sikkim transport office, they have a tourism dept office there. And you can catch a bus to Gangtok there, or a jeep from the road outside.(Hill Cart Rd, it's also the main road for Darjeeling.) Foreigners can only cross into Sikkim via the two crossing points north of Siliguri, Melli and Rangpo. So to get back to Darjeeling from North or East or West Sikkim you have to go round that way, then you can get a jeep down to Bagdogra airport and fly to Kathmandu.(via New Delhi) Certainly you've picked remarkable places to visit - the roads are rough (mostly) and steep in Sikkim, jeep tours north and east from Gangtok will be your best options there, probably.Everyone should visit Kolkata and Kathmandu once in their lives ! Best of luck.