There is so much to see in London, I tend to make for museums , rather than the shops, so many fantastic ones, I love The British Museum it's vast I could spend a week in it and still not see everything. The problem is the Egyptian rooms are sited on the ground floor and they are just sooo fascinating I get stuck there, but there is so much else to see, I particularly love some of the ancient Celtic artefacts too. Amazing place! The surrounding area of Bloomsbury is nice.
The Oxo Tower is great for panoramic views over London at night, especially St Paul's when it is lit up, but think you could see all of that walking over Waterloo Bridge especially if you are wandering back from Covent Garden which isn't far away. If you are going around Christmas time many of the landmarks such as the museums have pop up skating rinks which adds to the atmosphere and Southbank is also a good place to view all the lights.
V&A, Natural History museums also wonderful and such beautiful buildings. Also love the National Gallery and The Tate as well as The Tate Modern for art.
If you've got youngsters with you mine quite enjoyed Museum of the Moving Image when they were kids. Tussauds, from what I remember, there is an onus to hurry everyone through as quickly as possible, and I imagine it's very expensive, haven't been there for ages.
As far as shopping is concerned just be sure to avoid Oxford Street it's horrible but lots of other good suggestions here such as Libertys a lovely store. Harrods, when I last went it was something like a pound to use their loos
not that I'd buy anything there, very inflated prices as you'd expect.
I spent many years working up in central London, but haven't been up there since the pandemic hit. Before that happened we took several trips up to Hampstead Heath which is lovely and has great views over London plus the shops and cafes surrounding that area are nice but it's off the beaten track.
Wishing you a great time.