England trip between Glasgow, Edinburgh and Hadrian's Wall

My feeling would be that the cost of travel both in money and time between Glasgow and Edinburgh would offset any saving in cost of accommodation.

You should do the sums on the train fares back and forth and also consider the two hours a day of travel but it might still make financial sense. Many do it in August when all the festivals are on in Edinburgh.

Haltwistle may well make a good base for Hadrian’s Wall but don’t use it as a base for Edinburgh.

No doubt Stuart (isn31c) will be along with more advice on Hadrian’s Wall than I have.

Here's a suggestion, as a friend and I are planning to hike in the Lake District in northern England with a stop at Hadrian's Wall also in the itinerary.

You could use Keswick, England, as a base to visit Hadrian's Wall. Public transportation is available from Keswick to Penrith: Catch a local bus (like the 104 or similar) from Keswick Bus Station to Penrith train station. Penrith to Carlisle: Take a train from Penrith to Carlisle on the West Coast Main Line. Carlisle to Hadrian's Wall: From Carlisle, you can catch the AD122 bus, a key service that runs seasonally (typically spring/summer/autumn) along the central section of the Wall, stopping at major forts like Birdoswald, Housesteads, and Chesters.

You can save on accommodation cost in Edinburgh by staying outside the main tourist area. As long as you're on the tram line, you can get to all the sights much more quickly than you would on a train from another city. And the tram is £2, I think. I like Leith, for example.

Keswick is a lovely place to visit and well worth some time. But if your focus is visiting Hadrian’s Wall then stay at or very near it, not miles away.

Re- Craig's directions above, they are a wee bit confused. It is the X4/X5 bus from Keswick to Penrith, but there is also the 553/554 direct Keswick to Carlisle bus.
The AD122 only runs from the Roman Army Museum to Hexham via the wall. However we now have the new hourly HW1/HW2 bus from Carlisle to the Roman Army Museum. According to the County Council the two buses "kiss" each other at the Roman Army Museum. They certainly connect there, I haven't checked to see if they literally meet there.
As for commuting from Haltwhistle to Glasgow/Edinburgh it is possible, I do it from the Cumbria Coast, which is further. It is also cheaper from Haltwhistle to either than Glasgow to Edinburgh. However for a tourist it seems a bit far.
It is 30 minutes twice an hour from Haltwhistle to Carlisle by train, then hourly Carlisle to Glasgow or Edinburgh taking 70 minutes for the 102 miles to either city.
If you wanted to have one base for GLA/EDI/ the wall Carlisle would be more sensible. It's 40 miles from home so I don't normally stay in Carlisle but am in the middle of "test driving" most of the City hotels currently. I would have to say I am getting very good prices, and good hotels. I am quite impressed. Carlisle is a very interesting and historic city in its own right.
I would suggest basing in Glasgow for Edinburgh as Glasgow prices are usually way cheaper than Edinburgh.
Then for the wall choose between Carlisle, Haltwhistle or Hexham. Any will work handsomely. Another place which would work quite well is Brampton (use the bus 685 or HW1/HW2). The Scotch Arms Mews is probably the best place to stay in the centre of Brampton.

If you forced me to overnight in Edinburgh, then I too would choose Leith for value for money combined with convenience, but you would have to twist my arm hard when I can do so much better price wise in Glasgow.

Definitely stay in Haltwhislte rather than trying to do the Wall either from Edinburgh or Keswick.

Haltwhistle makes an excellent base for the best bits of Hadrian's Wall. The Old School House B&B is recommended. There is a lovely (easy) walk from Haltwhistle along Haltwhistle burn to the Milecastle Inn on the B6318. From there, take the unclassified road signed to Cawfields Crag picnic site rather than the footpath shown on the map. There is a lot of information about what to see on the walk up the burn here.

From the Cawfield Crag car park there's a short footpath leading up to the wall and a milecastle. If you want to walk, the walk east from Cawfields to Caw Gap is very easy and well worth doing with superb 360˚ views across Northumberland. It is one of my favourite short walks along the Wall. If feeling enthusiastic,/energetic you can continue east towards Steel Rigg and eventually Housesteads Fort. (There is a lot of up and down involved...)

You can also walk west from Cawfields which takes you past the unexcavated ruins of Great Chesters Fort and eventually Walltown Crags which is one of the highest and best preserved bits of the wall. The Roman Army Museum is only a short walk from here.

The AD122 bus can be used from Haltwhistle to access the eastern bits of the wall, including Houseteads, Steel Rigg and Vindolnda. . This is the stone wall which is better preserved than the turf wall which runs west from Birdoswald Fort.

There's a lot more information about Hadrian's Wall here- as well as other ideas of what to do and see in the area.

We toured the UK renting a car and stayed in Haltwhistle on a B&B (a farm), it was great.
Also, You won't need more than one day there.

We loved Durham and York. Edinburgh deserves more time than Glasgow. St. Andrews was worth a couple of days, especially visiting that area of Scotland.

Wasleys,

The AD122 bus covers the central part of the wall as far as Hexham. Then remains are often sketchy, but not non existent the further east you go towards Wallsend.

I am confused by this turf only wall beyond Birdoswald as that isn't so. The stone wall goes all the way to Bowness on Solway.

Initially yes there was a turf wall beyond the river bridge near Birdoswald but that was replaced with a stone one, often on a slightly different alignment. So in places you can see both. Especially between Lanercost and Birdoswald there is still a fair bit to see of the stone wall.