Travel Planning Paralysis

One way of looking at this is that if you end in York, there is a direct train from York to Manchester Airport every hour, which takes around 90 minutes or so.

If you go to Penzance from Bath there are flights from Newquay to both Manchester and Newcastle (Newcastle has a metro station, for the 5 trains an hour to York so NCL to York should be 2 hours or less.
Exeter Airport (possibly more convenient than Newquay, from Penzance) also has flights to NCL and MAN.

From Cheltenham then Bristol Airport is pretty easy to reach, for flights to NCL (and Bristol also has direct 24/7 bus service from Cardiff).

If you omitted York then there is the Peak District on the very edge of Manchester- very easy to get to.

Whether that is helpful in the slightest way I don't know. It may add to your woes.

Adding Paris as well is almost certainly over stretching it but most of the regional airports have flights to Paris, so it is not impossible, if pushing the envelope to it's absolute limits.

From Bath, if you want a seaside town, then Weymouth is an easy day trip by train, as an example rather than going all the way to Penzance. If I was just wanting a seaside town there are equally good options in Devon, to save a bit of effort in going all the way west.

London is fabulous, but it's easy to fly in and out of London, so you can get back there on a future trip without difficulty. I'd suggest keeping London to less than half the trip just so you can have a good variety of destinations. Maybe make a list of the things in London you and your daughter would be really disappointed to miss, then estimate how many days you'd need to accomplish them. If that turns out to be 10 days, so be it, but it probably will not unless (like me) you're see-everything-in-the-museum people.

Bath allows for multiple day trips, which is good. Keep in mind that Wells requires a bus and--unless you plan to rent your own car or plan to hike--seeing a bunch of the cute Cotswold villages will probably require a day-long van tour. Between Bath and Manchester you have Birmingham, Shrewsbury, Chester and Liverpool, among other places of interest. I liked Birmingham fine but definitely preferred Liverpool even though I have no interest in Beatles-related sightseeing. Shrewsbury and Chester have attractive half-timbered architecture. Chester works as a base for day trips into northern Wales, where you'll find nice scenery and castles. I loved Bodnant Garden, a wonderful National Trust property south of Llandudno Junction, and was able to get there in 2017 by public bus, though it wasn't a quick process.

I've only daytripped to Manchester (twice) but look forward to spending more time there. York is also great and offers good day trip possibilities to lovely rural areas and the coast. In case you are not aware, York and Bath are very touristy these days.

I'm lucky to be retired and can take longer trips, but I still face the same problem you're having, every summer. I focus on seeing as many things of interest as I can manage in a limited area, so I'm not spending so much time on transportation. You can use the National Rail website (https://www.nationalrail.co.uk/ to check on travel times. Sometimes stopping off in a smaller town between two large cities adds quite a lot of travel time, which is OK as long as you know that in advance and it's part of your decision-making process.

Edited to add: Isn31c mentioned Weymouth. I really enjoyed the Abbotsbury Subtropical Garden outside Weymouth. I remember having to walk some distance from the nearest bus stop back in 2017.

Right now, I have the following dates booked:

London May 27-June 2 (staying on points)
Bath June 2-5 (Airbnb I booked last December)
Harrogate June 11-16 (airbnb I booked last December)
16th travel to Mancheter to depart on the 17th (airfare is alread booked)

I chose Harrogate as it seemed like it might be a little calmer with good day trip options. For the train from Bath to Harrogate, I thought we could spend the day in York before continuing on to Harrogate. If we liked it enough, we could return from Harrogate
When I started to figure out where to go from June 5 -11, this is when my whole itinerary became overwhelming. Partly because I thought I wanted to go furher east past York so that seemed to be back tracking from Harrogate, but maybe it's not so bad to do that for a day trip. And then I second guessed myself that 5 days in Harrogate is way too long anyway So I could shorten it, stay in York for 2 days to go to Whitby.

But I have run into traveling quandries on going from Bath to Harrogate because I need to fill in 6 days. Stop at Chelthenham? Nottingham? Leicester? If I go further south, then the leg to York/Harrogate would be really long. But from the 5-11 is almost a solid week. Would Chester after Bath be too far before heading north to Harrogate/York? Which made me start to think maybe just skip Harrogare/York entirely and focus on areas around Bath before heading towards Manchester.

So that is why I came back to maybe I should just spend a full 10 days in London and go to Bath as a day trip, Windsor, Hampton, Hever Caslte, Kew Gardens, wanter around, maybe a day trip to Norwhich and then just take the faster train to York. I could spend 10 days in London on points which would be thousands in savings on lodging, leaving more $$ for food and sighte and trains.

I forgot about the airport in Newquay could be an option if after Bath we did spend some time in Cornwall.
I live in the middle of nowhere in California so anything is a welcome change for me. London would be the main large city of the trips and small villages towns after would be fine.

Which brought me to what if we headed south from London and made our way west towards Cornwall and up through Bath and ended in Manchester. I would have to cancel the Bath Airbnb and try to find other accommodations for an overnight as we pass through Bath and only stay the night there.

ugh

So that is why I came back to maybe I should just spend a full 10 days in London and go to Bath as a day trip, Windsor, Hampton, Hever Caslte, Kew Gardens, wanter around, maybe a day trip to Norwhich and then just take the faster train to York. I could spend 10 days in London on points which would be thousands in savings on lodging, leaving more $$ for food and sighte and trains.

I would do something more like this like Bath first from the airport for 2-3 days, take day trips to Stonehenge and the Cotswalds maybe. I've been trying to plan a 1st time trip to London with a 15 & 11 year old and 10 days would be very easy to fill, especially with visits to the castles. I just spent a week in Norwich last August and it was such an amazing historical gem, I would love to go back. I didn't make it to all the museums and the castle opened (after 5 years of renovations) the day after I left! :( You could easily spend a full day there not counting the 2-3h train ride there and back.

And then I think how cool would it be to go to Penzance!!

I love Penzance as a base for exploring West Cornwall - but unless you’re planning to spend a few days visiting St Michael’s Mount, Mousehole, Cape Cornwall, maybe the Minack Theatre, ancient stones, old tin mines, it’s probably not worth the trip as a destination in its own right.

There are plenty of great seaside towns all around the coast that don’t involve hours of travel to the far end of England.

Shrewsbury and Chester have attractive half-timbered architecture. Chester works as a base for day trips into northern Wales, where you'll find nice scenery and castles. I loved Bodnant Garden, a wonderful National Trust property south of Llandudno Junction, and was able to get there in 2017 by public bus, though it wasn't a quick process.

I am leaning towards Shrewsbury and Chester now. My daughter gets overwhelmed and doesn't have as much stamina to switch towns every 1-2 days. Although I am thinking of staying in Conwy, it seems we could make it a day trip from Chester. Or, take the direct train from Shrewsbury to Conwy for the night to see the gardens and castle and then make our way towards Chester. I do love the booking I have (refundable) in Harrogate though.

I too would suggesting swapping york with Chester. Similar in many ways and slightly easier with your travel plans. Direct train from there to Manchester airport.
You could take day trips to Liverpool and Llandudno/Conwy for Bodnant gardens. Maybe even an overnight stay.
If there are two of you, look at buying a Two together railcard for a 33% saving on off peak train fares. Cost £35 but may save you more.