I live near Oxford, was at University in London (40 years ago though) and have a daughter who lives on Anglesey where we holiday often.
I can endorse Blenheim Palace as a good place to visit. Oxford has the Ashmolean and Pitts-Rivers museums, both brilliant IME.
Anglesey is lovely and the Plas Newydd house, National Trust, is great to visit with a super history, it being the home of Henry William Paget, born in 1768, most famous for leading the cavalry in the Battle of Waterloo 1815, he lost a leg and was awarded the title ‘Marquess of Anglesey’ for his bravery. The story goes he looked down and said "Legs gone" to which another said "so it has sir" He is reputed to be the first person to have an articulated wooden leg.
Whilst in London I spent days in the 3 museums near me, Natural History, V&A and Science museum. Loved them all but haven't been for years.
I love North Wales and my favourite Fish and Chips restaurant is in Conwy, it still fries in beef fat - sadly rare now - so it tastes like the real thing to me.
I visited the George and J G Smiths distillery on Speyside with my in-laws to be in the mid 1970s but hadn't been to another until a couple of weeks ago we went to "The Macallan" new distillery which has been laid out with tours in mind. Expensive stuff though, I enquired about the bottles on sale from my and our friends birth dates, between £8,000 and £25,000 per bottle apparently. Temptation easily resisted.