In reply to subtle:
Museum-wise I'd go to the British Museum and the V&A before the others but with kids it might be different. As a kid I always loved the Science Museum for the interactive exhibits and National History Museum for the dinosaurs. London Zoo I think is old-fashioned and average. In South Ken, Rocca is a fun and reasonable pizza place.
A wander round Kensington Gardens at the palace end is interesting and calmer than many other parts of central London. The road leading up from Kensington High St to Notting Hill has many foreign embassies on it in palatial buildings. Around there, The Churchill Arms is a good pub that does good (and cheap) Thai food. Also around there is the Leighton House Museum which I quite rate though not free.
Another interesting place to wander round is Temple and the Inns of Court off Fleet Street. A different world from the hustle and bustle and a vision back into an older London. Around there Sir John Soane's Museum is brilliant though tiny and I think would be fascinating to a child. Round there, Ye Olde Cheshire Cheese is an old fashioned pub worth a visit and does OK basic pub grub.
In my view one of the best views in London is walking across Waterloo Bridge. Great sights in both directions. Good in day and night.
Out of central London, Hampstead is picturesque and worth a visit on a longer trip, there are good views from Parliament Hill on top of the heath. Excellent for flying kites. Greenwich and the Admiralty Museum also a pleasant excursion out of central London.
Spitalfields market worth a visit for food if you want to trek a little way east. The Ethiopian vegan stall is great, as is the rotisserie chicken place.