OP, meant kindly but a lot of those are the 'tourist hell / rip off' kind of places... I say this as a lifelong Londoner.
Not sure how long you are staying... also sorry for repeating some of the suggestions but...
Highly recommend a boat trip along to Greenwich - the market, park, Cutty Sark and Royal Observatory. There's a cable car over the Thames nearby - the boat also goes along that way. Boat and cable car can both be paid for using touch in/out debit cards, although the kids' tickets should be cheaper, so worth buying those separately.
Tower of London is wonderful. I also like Hampton Court if you like the Tudor period in particular. Kew Gardens is beautiful if anyone is into nature-type stuff.
The view from Primrose Hill is stunning, you can see the whole of London. It's also very close by to the zoo, if you like that sort of thing. Camden is also close by but in my opinion it's a shadow of its former self.
Portobello Road market on a Saturday is good.
One of the best ways to see London is on foot, providing no one has mobility issues.
It's really nice just walking along the river from Westminster (south side / London Eye) towards London Bridge, and you will see SO many sights.
Also there's a nice cluster in 'the City' of St Pauls's, with a really good view of it from the top of One New Change shopping centre close by. Also the Sky Garden (free but need to prebook or the queue is often big), and Fen Court Garden (free, rooftop garden with amazing views). In the basement of the Guildhall Art Gallery (close by) there's the ruins of a Roman Amphitheatre (also free) and the ruins of the Mithraeum are close too (also free but often booked up so need to prebook).