I always think the best way to discover London is to walk and head off into any interesting square or street that takes your fancy. One more mainstream walk is to start at Pimlico tube and head down to the river and walk to Tower Bridge (crossing the river at Lambeth Bridge. Then you can dip into whichever museums/attractions take your fancy - London Eye, Acquarium, Tate Britain or Tate Modern, Garden Museum by Lambeth Palace, medical themed museums at Thomas's and Guy's Hospitals, Film museum, Southbank Centre, shops at St Gabriel's Wharf and the Oxo Tower complex, the Globe, HMS Belfast and Borough Market..... You get great views across the river too.
If you like museums then it depends on your interests so I've tried to sort by subject:-
Agree with the Geffrye - also Soane's house on Lincoln's Inn Fields if you like interiors and Denis Severs House in Spitalfields.
For medicine and science the Wellcome Library opposite Euston is good too - a couple of exhibitions and a funky reading room and a nice cafe/restaurant/tea room upstairs (not the one in the foyer). It also has a lot of interesting talks in non-Covid times. ALso the Old Operating theatre by the Shard, Florence Nightingale Museum at St Thomas's hospital and the Grant museum of zoology in Bloomsbury. If you are in Bloomsbury then ELizabeth Garrett Anderson museum is small but interesting.
For music both the Royal College and Royal Academy have historic instrument museums which can be coupled with free lunchtime concerts (again not with Covid)
For fashion Zandra Rhodes Fashion and textile museum in Bermondsey
Heading out of the centre can be good - lots to do in Greenwich from the observatory and planetarium, the fan museum lovely cafe in the orangery) Royal Maritime museum and just a wander round the market and old naval college buildings. If its a nice day it is a good trip there by boat and back by DLR through Canary Wharf.
Dulwich has a lovely art gallery and a nice park and West Norwood (or any of the other Magnificent Seven cemetries) a suprisingly good walk with a mini Acropolis of Greek temple style mausoleums.
Finally, if your daughter is not too easily embarrassed there is the Vagina Museum in Camden - perhaps the less said the better.......