looking for advice for the order of Chester, Liverpool and North Wales from Bristol

Sorry, I said east side I meant west side of course.

The most efficient way is train Bristol to Newport, change, train bound for Holyhead to wherever in North Wales you are headed (if Conwy, get off at Llandudno Junction then cab/bus/walk across the bridge), then retrace your steps to Chester for however long you want there, then Merseyrail frequent train Chester to Liverpool.

** That would be your normal route. Tomorrow most services are trains to Manchester Piccadilly, switch trains at Crewe for North Wales**

After Liverpool, for the Lake District, an hourly train (bound for Blackpool) Liverpool Lime Street to Preston. Change trains.

** There are 2 or 3 through Transpennine trains daily from Liverpool to Edinburgh which avoid the change at Preston for Oxenholme and Penrith**

If heading for the South Lakes- on 2 of each 3 hours take an Avanti or Transpennine train to Oxenholme, change there (cross platform change) for the shuttle to Windermere.
Every 3 hours Northern run a train direct from Preston to Windermere.
If heading for the Northern Lakes stay on the Avanti or Transpennine train to Penrith, then the hourly X4 or X5 (on alternate hours) from straight outside the station at 20 minutes past each hour takes you to Keswick in 50 minutes for £2.

PS the U boat at Woodside Pier (use Hamilton Square, Birkenhead station) has been closed for a while now.

Thank you camborne1962, I return home Oct 31. I'm doing a loop around England and Wales I've "done" the Southwest, now going up the west side to Lake District, over to Hadrians wall to Durham, to York, then down to the Oxford and area usual suspects, then down to the South East. Leaving London till last and will miss it if necessary, as I've been before and can see it later on another trip via the Chunnel from the Continent when and if I go visit Holland/Belgium someday.

Thank you isn31c, I always look forward to your answers as they are very informed and helpful. Thank you so much.

By the way, if you are trying to do Hadrian's Wall the week after the one coming be aware that there is a scheduled bus strike in the North East all week. If the strike goes ahead there is an emergency, very limited AD122 bus running for the wall. Details are on this thread- https://community.ricksteves.com/travel-forum/england/go-north-east-buses-strike-action

Thanks again isn31c.
Good grief, I might have to wind up renting a car again after all. Hopefully there won't be a shortage of them.