The best thing about any charity shop is that you never know what you are going to find. I have a well tested route around London that includes all of my favourite charity shops. This Oxfam has a great selection of books and often turns up some interesting clothes too.
The Design Museum is a museum in Kensington, next to Holland Park, which covers product, industrial, graphic, fashion and architectural design. There is also a nice cafe on the 1st floor with beautiful views of the park.
The walk along the South Bank from Westminster to Tower Bridge will take you past a plethora or interesting sights and cultural hotspots. There's always something interesting going on too.
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.