Not the most exciting place inside, but a lovely rooftop area which not all that many people seem to know about, 2 mins walk from Old St station. If it’s packed then The Red Lion is just up the road.
Appreciate the 'bar hidden away behind a bookcase' thing is pretty naff but the cocktails here are unreal (try the Hot and Cold), and it's inside Milroy's Soho, one of the most legendary spirits stores in the city
The Wellcome Collection is a free museum and library, mostly dealing with medecine and social history. The exhibitions are unusual and engaging, and the permanent collection includes bizarre items such as medieval masks and human remains.
Being down on the underground can be quite stressful and draining, but if you have the chance to look up and into the details that has gone into the tiling of the platforms and stations you might start to see some beauty down there. A lot of stations has bespoke tiles and decorations, almost a century old.
Bethnal Green station is one of a handful in London to have been given a very specific additional decoration to the classic cream tiles and name strip. Easy to miss, but dotted around the station are a series of tiles with raised motifs on them, representing aspects of London and places that the Underground visited.
Or for typographers: check the type on Hampstead station or Holloway Road for some inspiration.