I will be traveling from Edinburgh to Durham by train and have to return that night. I would like to see Durham Cathedral and travel on to Beamish Museum. I understand that direct buses (no transfers) run on Saturday. Buses with changes run during the week. Questions: (1) Cost of taxi vs. inconvenience and travel time of bus with/without connections and (2) Is a visit to Durham Cathedral and Beamish Museum doable in one day in the middle of a round trip train from Edinburgh to Durham/Beamish Museum. Thanks in advance for any thoughts/suggestions Frank
You can't see all of Beamish in one day, let alone combine it with Durham, which is c 2 hours each way on the train from Edinburgh. Beamish is c 30 minutes drive from Durham, so even by taxi, a return trip would add an hour to your day before you even entered the museum.
I suggest that you just cover Durham.
Given the fact that you have to travel from Edinburgh and back again, I would recommend spending your time in just one of those places. It's a case of what you would prefer to see more: an historic town, or local interactive Victorian history. Beamish would require you taking a taxi from Durham station, while you can just walk from the station into the city of Durham.
I've done both and if I had to pick one it would definitely be Beamish.