Chester or Windermere

That is impossible to say. Remember two nights only effectively gives you one full day in a place.

Have you worked out what you are wanting to do in all these places and how many days you will need? This depends on your interests and what you want to do.

No experience with Chester but spent several days in and around Windermere on one trip and a through walking tour that included a night in Grasmere.

Two nights in Windermere may be short depending on what you want to do and see. You could spend a day exploring the Beatrix Potter Lake District:

https://www.nationaltrust.org.uk/beatrix-potter-gallery-and-hawkshead/features/beatrix-potter-the-lake-district-and-the-national-trust
https://www.nationaltrust.org.uk/features/beatrix-potters-hill-top
Take the ferry across the lake then a walk or bus to Hilltop:
https://www.windermere-lakecruises.co.uk/cruises-fares/bowness-to-ferry-house-cross-lakes-shuttle

Or if you are into Wordsworth poetry, there is Grasmere, a bus ride or nice country walk from Windermere:
https://www.visitcumbria.com/amb/grasmere/

Chester is a Walled City with a Historic Roman relic architecture and restored Tudor era timbered Shopping District. We've enjoyed it both times we stayed there. If you fly into Manchester it is a great place to get ready for your train trip. You can "taxi" or bus there from the airport. You can take a day trip to Conwy or Liverpool from there. In the Lake District you have to climb to get a good view of the Lakes, or take a boat ride; the Hotels seem to own most of the shoreline in Windermere. I would spend more time in York and environs, Bath, Portsmouth (ships Mary Rose and Victory) and of course London. Stratford is a good place to spend the night if you are going to a play. London accommodations are more spendy, but there is a ton of stuff you can do for free.

I’d do 3 days in Liverpool with a day trip to Chester which is very easy. I enjoyed a day in Chester but not sure I’d want more than that.

I wouldn’t want less than 3 nights in Chester as it’s a good base to see Liverpool and North Wales plus the city itself. Three nights is only 2 days.

I wouldn’t go to the Lake District without a car, as I prefer to get away from the crowds of Windermere, Keswick etc by heading east, but Windermere will give you a flavour of the area and two nights gives you enough time to take a boat trip and maybe a short walk.

I find Stratford upon Avon tacky and disappointing. York is worth a 3 night stay.

Be careful about what order you intend to do your trip. Stratford-upon-Avon is down a dead end and it is not easy to go by train from there to Bath, for example. (You would probably need to go via Oxford - that being so - you might as well see Oxford). Bath to Portsmouth is easy with 1 train per hour BUT they go through Salisbury - well worth seeing the medieval cathedral or even taking the shuttle bus to Stonehenge. So, you could be travelling through places of interest without seeing them! Also note that Chester to Conway (Conwy) is well worth the trip but is easy from Chester - a bit less so from Liverpool.

I suggest you check the schedules at www.nationalrail.co.uk but bear in mind that for longer train trips, it pays to pre book specific trains in Advance - and these cheaper fares gat loaded around 11 weeks ahead. Also consider a 2 Together Railcard - which you can get on arrival but still make the Advance purchases as if you already have. (Not valid before 9.30am on weekdays). For short hops - such as Chester to Liverpool return - pay on the day.

On some routes, it pays to split the ticket. (Manchester is usually a good place top split if passing through to reduce the price). This site is good at telling you the splits:> https://www.traintickets.com

Start by looking at this map of the rail system:>https://www.nationalrail.co.uk/Rail%20map%20v31%20December%202019.pdf

We did a wonderful four week drive tour of S. Wales and England in October 21017. I wanted to do Chester, but it was a bit out of the way. Had previously been to Liverpool and N. Wales. Liverpool was OK, but not into Beatles tours, but N. Wales was great (did in 2014). S. Wales was equally great, which we did in 2017.

Stratford Upon Avon was wonderful, but I am a huge Shakespeare fan. I highly recommend that city and to do all five of the Shakespeare sites.

We spend 3 nights in Keswick in the Lake District. The scenery is wonderful, but it was late October by the time we arrived, so we didn't spend a lot of time out of doors. It was windy and cold. We did a nice drive around the lake next to Keswick.
It is an effort to get to the Lake District, but if you only go for two nights, perhaps you should skip it.

Bath was great, we spent three nights there and after doing Bath and the wonderful Roman Bath Museum and a walking tour, we spend another day going to Wells and Glastonbury. Wells was nice with its small cathedral. Glastonbury was good, but now the WOW factor.

York was one of our favorite cities in the UK. We spent three nights there and loved every minute of it.

Here is my review with details of our trip. 28 days in Britain and Celebrity Eclipse home
https://www.cruisecritic.com/memberreviews/memberreview.cfm?EntryID=599139

I would go with Chester over the Lake District. Durham would be high on my list as well.

Thanks to all of you for your excellent advice. We appreciate it very much. D&B

Many people come to the Lake District for one day and decide that they should have spent a lot longer here. It is England's largets National Park at almost 900 square miles. There is a lot to see!