Edinburgh

Linda, do you know there is a Scotland Forum here devoted to questions about the place?

https://community.ricksteves.com/travel-forum/scotland

This question has wound up in the General Europe area - for general or broad questions.

Regarding places to stay there were answers in your post four years ago - might be a place to start while waiting newer answers.

https://community.ricksteves.com/travel-forum/scotland/124542

Saint Andrews, play on the Himalayas putting course. It just costs a pound or two and is so much fun. You will see the golfers on the old course 50 feet away from you playing after paying big, big bucks. I doubt they are having any more fun unless they are serious golfers. A great activity that provides fun memories and is very low cost.
http://www.visitstandrews.com/do/great-outdoors/2643-2/

Stirling Castle. I liked it much better than Edinburgh Castle
https://www.stirlingcastle.gov.uk/

Falkirk Wheel. Modern engineering feat that allows to canals to connect via a large wheel. You can ride a canal boat up the wheel and then down a canal a short ways before returning and riding the wheel down again.
https://www.scottishcanals.co.uk/falkirk-wheel/

We stayed at the Premier Inn in York Place. Very reasonably priced, very clean and modern. Top floors have a gorgeous view out over the Harbor. Ask for a room on that side. Currently showing 84 pounds a night for the last week of June. The tram to/from the airport stops directly in front of the hotel and runs about every 10 minutes.

Saint Andrews is convenient and there's a castle ruin there (plus golf)