arriving in London last week in April - plan a 2 week trip

When you say rail pass I'm not sure if you mean rail pass or rail card.

There isn't a railpass which is worth it for your journeys. But, regardless that you are both over 60. buy a Two Together Railcard, to give you 34% off all rail fares (including the cheap advance fares). Use the 2T as that costs £30 for the two of you; senior railcards will cost you £30 each.

I'll let Mardee give you some great advice on a stop in Northumberland.

This won’t help the poster but Jetblue are introducing JFK > Edinburgh flights from the 22 May 2014 to the end of September.

2 train companies operate between London King’s Cross and Edinburgh = LUMO & LNER. The most obvious place to have a stopover on this route is the historic city of York and LUMO don’t stop at this city. Pre-book Advance specific train tickets around 10 weeks out for the odds of the cheapest fares.

https://www.seat61.com/london-to-edinburgh-by-train.htm

As the OP has specifically asked for a stop in Northumberland Lumo do stop at Morpeth, which is useful for buses to the coastal parts of the county.

But they run very few services per day. So if they cancel a train you have a long wait. And probably won't get a seat on the next train.

From Morpeth to Edinburgh TransPennine also run, and often have the cheapest fares for that sector. Cross Country also call at Morpeth, plus a very few LNER trains a day, plus an hourly Northern service from Newcastle.

And Lumo (and also Grand Central) have both had very critical accident reports, in cases of severe over speeding which very nearly led to a derailment - caused by poor driver training.

My feeling is that the border town of Berwick on Tweed would be a good Northumberland stop over. A very interesting and historic town, and buses from there down the coast. At Berwick the buses leave from outside the station. At Morpeth it's a short walk down the hill (not bad, but a bit inconvenient, especially with luggage).

You don’t say how long you are planning for your stop in Northumberland...

Berwick would work well as a stop - it’s an interesting town with an equally interesting history - it regularly changed hands between the English and Scottish. It has Elizabethan walls and the scant remains of an earlier castle. There is also the Barracks Museum and Main Guard too. The three bridges across the river are stunning and there is the harbour area to explore too. There are ideas for walks around Berwick here.

I personally would discount Morpeth. If you want a base further south, then I would suggest either Alnmouth which has a railway station or nearby Alnwick (bus from Alnmouth and pronounces An-ick.) Alnwick is very much an unspoilt market town with the castle (still the home of the Dukes of Northumberland) as well as the gardens which were the vision of the Duchess who not only wanted to bring a derelict walled garden back to life but also provide much needed employment and a community resource, with its drug awareness programmes and work with dementia sufferers. The result is possibly the most ambitious contemporary garden in the world, with its cascade, water features and poison garden and the world’s largest tree house. They are wonderful. Don’t miss Barter Books in the old station buildings either! If you want to stretch your legs, there are ideas for walks here.

You could always save time on your return from Edinburgh back to London by catching the Caledonian sleeper train...