travel to the Lake District, the Yorkshire Dales and Edinborough

If you are flying from the US, you could fly into Edinburgh, then train down to York and take tours of the Dales, then train over to the Lakes. From there you can train up to Manchester and fly home from there

I’m going to throw another idea out there.

I really want to go to the lake district, but it seemed difficult using public transportation. So, I plan to sign up for this tour from Edinburgh:

https://www.rabbies.com/en/england-tours/from-edinburgh/3-5-day-tours/the-lake-district-3-day-tour

For tours from York, I took these two last year and loved them both:

https://www.mountain-goat.com/Yorkshire/Scheduled-Tours/North-York-Moors-and-Whitby

https://bobholidays.com/tours/herriot/

Good luck with the planning.