NB: The rail fares below assume that you've got a Senior Railcard. If you haven't, either consider getting one (£30 for a year or £70 for three years) or add roughly 50% onto all of the fares I've shown:
Based upon the prices currently offered for a fortnight earlier than you want to travel (which is the last weekend for which tickets are currently available), outbound travel to London is available on the Friday for just £19.50, if you're a real early bird, at 0655 (getting into Kings Cross at 1003). Travelling later, at 0802 (and getting into Kings Cross at 1053) costs £37.95. There are similarly priced tickets available later in the morning too, plus an option to pay £25.45 for travel at 1058 (arriving Kings Cross 1353).
If you attend the 3pm performance on the Sunday (which finishes at approx 5.35pm) you'd have plenty of options for return travel. Ticket prices for Sunday evening travel aren't currently shown for the sample date I'm using (24 Oct) but bringing the date forward to 3rd October suggests that you might have to pay £50.25 for travel at, say, 1930 (getting back to Newcastle at 2346).
If you stay overnight on the Sunday, there are loads of departures available on the Monday for just £19.50. (So you could either return early on the Monday or do lots more sightseeing and head home much later in the day).
Whatever you do, don't pay for your rail travel on the day, as it'll cost you a whopping £521 (plus another 50% if you've not got a Senior Railcard)!
Check your times, and book your tickets, either here
https://www.nationalrail.co.uk/
or here
https://www.lner.co.uk/
(Do NOT use other services, such as The Trainline, as they can't offer you any cheaper tickets and usually add a booking fee on top of your fares, costing you MORE).
The best to time to book will probably around the end of this month, as fares for your chosen dates should be online by then.
I'll now start thinking about hotels ;-)