Ask HN: Where in Ireland or the UK should someone visit that most tourists miss?

My mother will be traveling there this June for three weeks. This will probably be her last vacation, and I really hope she loves it. She's always wanted to visit Ireland and the UK as much of her family's heritage originates there. When visiting foreign countries, she really enjoys spending most of her time observing the culture outside of tourist hot spots.

More details: She plans to visit London, Wales (I don't know which city), Nottingham, Edinburgh, and Stonehenge or another henge. She'll be in Ireland for about a week, but isn't sure where to go outside of Dublin yet. She'll be traveling with three of her sisters and a friend. They plan to rent a car. She doesn't drink alcohol. She prefers BnBs to hotels, and I've shown her how to use Airbnb if they don't find a vacant BnB where they plan to sleep.

I would greatly appreciate if anyone from or familiar with these countries could offer any tips, suggestions, or warnings.