So my Dad was a command pilot with more than 5600 hours of flight time and four years served in Vietnam. I asked him about the C47's and how they made it across the Atlantic and Pacific. He sent me what I found to be a really fascinating answer, so I'm just going to post the whole thing below - everything else in this is from him:
The C-47 carried between 2,000 and 2,200 gallons of fuel in four wing tanks. That gave the bird a range of about 1,600 statute miles (the miles we drive on the highway) or about 1,390 nautical miles. (The statute mile is 5,280 feet long while the nautical mile (which is used for air and sea navigation) is 6,080 feet long. I’ll come back to this later.
Four additional fuel tanks containing a total of 800 – 820 gallons could be installed in the passenger compartment to extend the range to 3,600 statute miles or 3,100 nautical miles. The weight of those tanks limited the total number of people on board to no more than about 5 – essentially the flight crew and its crew chief.
The most likely route for the transatlantic flights would have been up the east coast of the US, with stops either at Gander, Newfoundland (where all the US-bound airliners from Europe were diverted following the 9/11 attacks on the US) or Goose Bay Labrador (I’ve landed at Goose Bay). From there, stops in Greenland, Iceland, either Shanwick, Ireland or Prestwick, Scotland and then on to final destination.
For the transpacific route I am guessing that it involved stops in Hawaii, and then there are all sorts of places from there to the Asian coast – Wake Island, Midway, Guam, Philippines, etc. and then on into Asia.
Nautical miles are used in air and sea navigation because 1 nm = 1 minute of latitude. The distance from the equator to either the north or the south pole is 5,400nm. That equals about 6,200 statute miles which when multiplied by 4 equals just about the circumference of the earth as we know it to be.
In the mid-60s I had the chance to check out in the C-47 and maintain my T-28 certification at the same time. Glad I did not pursue the C-47 as I would most likely have been flying that in Vietnam; I viewed my chances of survival MUCH better in the C-130.
Again, great question – fun doing the research!