Ideas for a rare day off in London, please!

[BoudiccaRuled]

I'm looking for memorable places to go with an old friend, just one day, midweek in early December. We are into culture and books, used to spend a lot of time smoking, discussing existentialism and generally being pretentious in cafés before kids and reality came along.
Not interested in going to a show or trawling high street shops, if that's even still a thing.
I know there are wonderful "hidden gems", please can those of you in the know share your best with me?

Not sure if they're exactly hidden, but Daunt Books and the Wallace Collection are in Marylebone. Loads of cafes in the area. And you could see what's on at the Wigmore, as well. Have fun!

I have a week off in mid-December. I’m planning a trip to the Wallace Collection and a stroll around Marylebone one day and then a trip to the Turner & Constable exhibition at The Tate on another day.

The V&A cafe is very nice to hang out in, sometimes there's live piano there. Leighton House is gorgeous to visit, and Denis Sever's house is worth a visit, near Spitalfield market and some great pubs.
I also really like this pub for lunch Lambs Conduit Street.

Funny my first thought was the Wallace Collection and Daunt Books too. They may not be hidden gems exactly but the Wallace Collection was not overcrowded when we were in.

Also not a hidden gem but we thoroughly enjoyed Frameless.

I love a trip to the British Museum then a glass of champagne in their lovely cafe under the amazing glass roof.

The Sir John Soane museum near Holborn is definitely a hidden gem.

Dennis Severs house! Magical especially as they’ll have decorated it for Christmas.

https://www.dennissevershouse.co.uk/

The Christmas decorated 'Rooms through Time' at the Museum of the Home.
Winter Past - Museum of the Home

I went there a few months ago and definitely want to go back. An astonishing place!

The Foundling museum. Just down from kings x...very moving and definitely worth a visit...take hanky.