What everyone else here has said. Last year, I was in London for work, and then "popped over" to Paris for the weekend. It worked for me as I was NOT doing touristy things. I was just wandering, shopping at brocantes, other shopping (but of course!), drinking great wine, and having great meals. Other than a few planned meals, I had no plans, so that worked out really well, as the weather both times was pretty shitty (rain is omnipresent in March and April in both London and Paris).
If this is your first time in London, I would do Manchester for 2 or even 3 days (I think there might be some cool stuff in Manchester, but I have not been that far afield yet), and then spend the rest of the trip in London.
My recommendation to everyone is to plan one thing for the morning (or a couple of things if they are REALLY close together), and then one thing in the afternoon. Give yourself plenty of time to wander, pop into a pub and have a pint, and just marvel at the cool shit in London.
If you stay in London longer, you would have time to go out to places like Windsor (cool pubs, but honestly kind of meh (I worked for a company HQd there, so spent a lot of time in Windsor)) and Hampton Court (this I do recommend as it is really cool).
As for restuarants, Fallow and Brat are both very good. In 2024, I did: Sunday Roast @ The Devonshire, Grazing Goat (Pub), Brunswick House, Speedboat Bar (Thai), Yashin Sushi, Dim Sum Duck (lines are atrocious), Zephyr Notting Hill, Caravel, Gordon's Wine Bar (celebration with the team, lots of wine, good cheese and meat), another Sunday at the Devonshire (but steaks this time vs. a roast), The Barbary in Convent Garden, Manthan, Kinkally (Georgian Dumplings), Noble Palace (team lunch), Kurisu Omakase, Dovetale, Paradise Green (Aussie resto), Mina's (team lunch), The Dove, Hammersmith (old school pub, definitely good food), Bibi (I went to Gymkhana in 2023), Mambow (probably the best place I went in London in 2024), The Swan in Milton Keynes (boozy Sunday Roast with friends), Mamapen (only Cambodian resto in London - Currently a pop up at The Sun & 13 Cantons pub - really, really good), and Kol (absolutely fantastic haute Mexican). I think the best meals I had were Mambow, Kinkally, Kol, Kurisu Omakase, and Caravel as the top 5. The Devonshire was really, really good, but I can have amazing steak here in NYC. The Dove was very good for a pub.
With kids, I think Kinkally could be fun (Georgian Dumplings are awesome). Mambow is a bit further afield, but worth the hike, IMO.
As for activities, if you are going to do the changing of the guard, skip Buckingham Palace and do Horseguards (see Westminster Abby afterwards). The Houses of Parliament are fun to go into (love seeing Westminster Hall), and can also be paired with Horseguards, and Westminster Abby (I did that same route with my folks in 2017 - we had a big breakfast, and then did things for about 5 or 6 hours, then had afternoon tea rather than dinner).
I love the Tower of London, and it has been years since I have been. I might be due for another visit.
Borough Market is always good for a few hours. Leadenhall market is another area I recommend, though I have not been in years admittedly.
London has amazing museums, and I personally think that the National Portrait Gallery and the National Gallery are all worth stops, as is the V&A.
I am starting to plan out my work trips in 2025, which I am sure there will mean 4-8 weeks spent in London. Definitely work on your wife to convince her to slow things down.