As above, the Museums are a must.
For food, I can very much recommend Sophie’s in Covent Garden as one of the best kid-friendly restaurants that’s also a nice place for grown ups to eat. Don’t take bookings, though, so get there a little early if you can.
Top tip – The Number 11 bus. Runs from Chelsea, through Westminster and in to the City, past all the sights.
Have a look at the Tate as well, the proper one! They do a lot of great events for kids, that really get them involved in the art. Plus, you can pop over the road for a great beer in my local…! 🙂