Itinerary order - when to do London, when to Go Elsewhere

First time poster with basically 5 days in London.

Is my math correct?

You’ve stated you’ve been before. What have seen?

Scarborough is a good 3.5 hours by train.

As far as theatre:
Witness for the Prosecution
The Play That Goes Wrong
Wicked
Hadestown
Mrs Doubtfire

Yes, first-time poster.
Up to five days in London, but on this trip I'd be interested to spend some of them elsewhere (including nights on a sleeper).

Past trips have included the British Museum and Library; the Globe; St Paul's; Westminster Abbey (very briefly); Churchill's War Rooms, and time spent memorial-hunting on the Embankment. Last round of shows included As You Like It, Macbeth, Pygmalion, Private Lives, Little Big Things, Frank & Percy, and Crown Jewels. This time around I'm thinking about Austentatious, Starlight Express, Our Country's Good, and a production of Bedroom Farce in Reading.

Then take the Eurostar to Paris.

Or train to Edinburgh.

Or train to Whitsable or Rye or Eastbourne or Brussels.

If you have so little time [two nights?], it would make sense to plan your extra time in the same direction as the route to Scarborough.

York is the no-brainer - it's very popular with the forum folks here [not so much with me], but the railway museum is certainly worthwhile, and it is fun to walk on top of the walls for a bit.

A bit farther afield in the same general direction are Durham and Newcastle upon Tyne.

Edinburgh also to a degree, although travel time will eat into your schedule. And there is the Caledonion Sleeper from London, per your comment.

If it were me with those time commitments, after landing in London I'd head to York for those couple days before going on to Scarborough.

If you want to take in some little bit of Wales, you could go from London to Manchester and while in Manchester schedule a tour with a company like Rabbie's for a day trip to Snowdonia & north Wales -- https://www.rabbies.com/en/england-tours/from-manchester/day-tours/snowdonia-chester-north-wales-1-day-tour -- then on to Scarborough. Though a journey from Manchester to Scarborough is nearly 3.5 hours with 2 changes.

Begin in London to recover from jet lag and to hit the sights. Possiblywith a a day trip to Bath, Oxford both easily reached by train for the day. Then head to Scarborough.

Then either York (much more to it than the railway museum and a walk along the walls!) or up to Durham (cathedral, castle, Crook Hall Gardens, walks along the river ...) on the way back to London.

You don't really have time for Scotland, Wales or France in the time you've got available with the time commitment of Scarborough in the middle.

Thank you all very much! This is a lot to chew on.

Would a trip to Edinburgh or Cardiff or Paris be more practical to attempt if I did it after Scarborough, with the plan to get back to Heathrow for a 10am flight on the 19th?

The morning of the 16th, Edinburgh is approx. 2-1/2 hours by train once you get to York. Mid afternoon on the 18th take the train from Edinburgh to London, then directly to a hotel at LHR for your morning flight.

Practical? Only you can decide whether 48 hours in Edinburgh justifies the time on the train.

I'm not the biggest fan of York, although I liked it, and certainly York Minster is well worth seeing. It would probably help to know what you like to do (besides see shows).

If it was me, I would possibly head down to Oxford after Scarborough and spend a few days there (not sure how much you've seen of it), then head to London for your final flight.

Another idea would be to visit Newcastle, which is a pretty cool city. You could take a day trip to Durham Cathedral, which is worth seeing, and spend some time exploring Newcastle. You won't see many American tourists there (unlike York), so it's a fun city without huge crowds.