best day for pre-teens is Greenwich and then Canary Wharf for the docklands museum in my opinion
Take the boat to Greenwich from centre of town for extra fun!
Greenwich park is awesome - includes great play park,
royal museums at Greenwich website and take out probably the family membership ticket as it will cover a years worth for 2 adults plus 1 guest adult and 4 kids - is around £80 - covers all exhibition including planetarium shows.
planetarium is brilliant (they have special kids showings for under 7s and 7-12+), observatory fascinating if you have older kids (maybe from 8*)- it’s about the history of navigation and time, maritime is great with lots for under 5s in particular (ahoy, great Map, play gallery) but also lots of interactive things for older children and usually a few special events during holidays
Lunch at Franco Manca/Bills if you want a cheap kids menu or sticks and Sushi if you want to splurge
royal naval collage is quite interesting- now a university has an interesting “painted ceiling” room which you can get a tour of (inc in ticket price) and the building is regularly used as a film set. (NB the painted ceiling room is paid entry and not part of the royal museums)
Cutty sark is ok - not amazing but ok - worth popping in if you purchased the membership ticket
then over to Canary Wharf via DLR for the museum of London docklands, something nice for supper (ippudo noodles is pretty good). Canary Wharf also have lots of free family events - worth checking the website. Includes a family friendly music festival which was all free last year.
or you could take the cable car instead if the DLR from North Greenwich which could be great fun for views etc!
have fun!