The three things you already mentioned would be top of my list, too!

I'm most likely going to (moving to?) Wales sometime this year for a few months, so in a half-derail if we could expand this to "things to check out in the non-England part of Britain" that'd be cool.

I've spent quite a bit of time in England (like cumulatively 2 years) but all as a kid with my parents. So I guess if there's anything throughout the entire Kingdom other than stately homes that I should catch up on, please do sing out.