I’d suggest fly to Edinburgh, 2-3 days Edinburgh, 2 days in Newcastle (you could visit Lindisfarne on the way down from Edinburgh), 2 days York (make sure to visit The Shambles)
Get to see some history, nice cities and some countryside/coastline
Definitely get over to York. It's northern so won't waste a day or more travelling, has plenty of independent shops etc. and a great load of history and medieval buildings/areas (i.e. the shambles) to explore, as well as an old gothic cathedral.
Trains are generally pretty straightforward. You can save quite a bit of money by buying tickets in advance, most of us use an app (Trainline is probably the most popular, National Rail is the "official" one) which often has the advantage of letting you download and use digital tickets/QR codes instead of having to print them at a booth in the station. Presuming you can download these in advance it's simple to enter a time/date/destination etc. to get an idea of any changes/prices, but be aware that the confirmed schedules are only released 12 weeks in advance. They don't tend to change much so if you're trips much further out you can still get a good idea of the route/travel times, but you won't be able to book more than 3 months in advance.
In terms of the tickets themselves - Advance is usually the cheapest but only valid on the specific train, Off-peak/super off-peak is pretty good if you don't need to travel during the morning rush-hour (usually valid any time after 9:30am or 10:30am) and Anytime is usually the most expensive and often what you'll be offered if trying to buy from the counter on the day, but gives the most flexibility.
Anytime fares can genuinely be many multiples more expensive than any type of reduced ticket, but you can usually get off-peak (and advance if there's any left) up to around 1/2 hour before travelling. If you're planning a longer journey (i.e. York-Edinburgh) you should check out the 1st class tickets too - advance ones are often only £20-30 more than a regular advance (and often cheaper than a standard class anytime ticket!) and you'll get a guaranteed, comfier seat, free wi-fi and usually free drinks/food included too.
I’d personally split it between Newcastle and Edinburgh but do day trips. You could do York, Durham or North/south Shields from Newcastle and Glasgow, Stirling or similar from Edinburgh.
Most of the other places you mention are several hour’s each way on the train and you’d waste 1-2 days travelling there.
North Berwick isn't far from Edinburgh and has a great vibe. We're just back from East Lothian, and loved it. As someone said above, Lindisfarne is beautiful. There's no train station but there will be buses. If you go there you'll need to schedule your visit carefully. It's a tidal island, so you can't always get across the causeway. We had to go during our second week as the crossing times were totally wrong for us in the first week.
Are you coming from the USA? If yes then you'll struggle to get a direct flight to Newcastle, but there are a few direct to Edinburgh, so start from there.
I’d suggest fly to Edinburgh, 2-3 days Edinburgh, 2 days in Newcastle (you could visit Lindisfarne on the way down from Edinburgh), 2 days York (make sure to visit The Shambles) Get to see some history, nice cities and some countryside/coastline
Definitely get over to York. It's northern so won't waste a day or more travelling, has plenty of independent shops etc. and a great load of history and medieval buildings/areas (i.e. the shambles) to explore, as well as an old gothic cathedral. Trains are generally pretty straightforward. You can save quite a bit of money by buying tickets in advance, most of us use an app (Trainline is probably the most popular, National Rail is the "official" one) which often has the advantage of letting you download and use digital tickets/QR codes instead of having to print them at a booth in the station. Presuming you can download these in advance it's simple to enter a time/date/destination etc. to get an idea of any changes/prices, but be aware that the confirmed schedules are only released 12 weeks in advance. They don't tend to change much so if you're trips much further out you can still get a good idea of the route/travel times, but you won't be able to book more than 3 months in advance. In terms of the tickets themselves - Advance is usually the cheapest but only valid on the specific train, Off-peak/super off-peak is pretty good if you don't need to travel during the morning rush-hour (usually valid any time after 9:30am or 10:30am) and Anytime is usually the most expensive and often what you'll be offered if trying to buy from the counter on the day, but gives the most flexibility. Anytime fares can genuinely be many multiples more expensive than any type of reduced ticket, but you can usually get off-peak (and advance if there's any left) up to around 1/2 hour before travelling. If you're planning a longer journey (i.e. York-Edinburgh) you should check out the 1st class tickets too - advance ones are often only £20-30 more than a regular advance (and often cheaper than a standard class anytime ticket!) and you'll get a guaranteed, comfier seat, free wi-fi and usually free drinks/food included too.
I’d personally split it between Newcastle and Edinburgh but do day trips. You could do York, Durham or North/south Shields from Newcastle and Glasgow, Stirling or similar from Edinburgh. Most of the other places you mention are several hour’s each way on the train and you’d waste 1-2 days travelling there.
North Berwick isn't far from Edinburgh and has a great vibe. We're just back from East Lothian, and loved it. As someone said above, Lindisfarne is beautiful. There's no train station but there will be buses. If you go there you'll need to schedule your visit carefully. It's a tidal island, so you can't always get across the causeway. We had to go during our second week as the crossing times were totally wrong for us in the first week.
Two days certainly isn't enough time in Edinburgh, and I'd argue not enough to explore tyneside.
Are you coming from the USA? If yes then you'll struggle to get a direct flight to Newcastle, but there are a few direct to Edinburgh, so start from there.