My wife and I are planning our first international trip with a 13 day trip to the UK in May 4 - May 16, 2024. We'd like to see Edinburgh and London, but I'm unsure of what else to see. I think York in between would be nice, but what else? Flights are much cheaper flying in round trip to London, but I'm concerned about losing time going back and forth to Edinburgh. I had considered flying into or out of Edinburgh at either end of trip, but that will take more time with stops and cost $500-$1K more There is a fair priced direct flight from Atlanta to Manchester where we could then head to Edinburgh, but I'm unsure what there is to do around Manchester or Liverpool for 1 day as we adjust to time change.
Basically, looking for suggestions on what to see and how best to travel between Edinburgh and London. Part two, is there time to explore Scottish Highlands and York as well?