Greenwich if just for the view.
Tower Bridge Exhibit if not afraid of heights.
Evensong at Westminster Abbey, St Brides or St Paul’s
Enjoying pub grub at: The Dove, the Victoria Paddington, the Seven Stars if not allergic to cats,
or The Mitre Paddington.
I’ve not taken the tour and if Hampton Court isn’t included definitely add it to your itinerary. Add Shoreditch for the street Art.
Don’t miss seeing theatre and definitely venture outside of London. Richmond park is wonderful especially the free roaming red and fallow dear. The silver vaults are interesting, the Sir John C Riblat room in the British Library ( the Treasures Gallery ) is wonderful.
Personally I also love the dichotomy of the architecture:
The Gherkin near Leadenhall Market
The Blackfriars pub across the road from Blackfrairs station.
If walkers the Park Land trail is really nice. Tube to Crouch Hill. Walk back towards the old dairy. Fabulous exterior art work. Cross the road and grab a coffee and then head out to the Parkland Trail. Really really nice, joggers, walkers, dogs on leash…Excellent way to “ blend in” exercise and relax.
I throughly enjoyed the uncrowded Hunterian Museum. Avoid if you see school busses.
A stroll from Marie’s deli in Chiswick along the Thames path to Hammersmith Bridge is pleasant meander.
Honestly, been visiting London for 50 years. So much to see and do and explore. Have a great time.