With the nine-year-old in mind, the Rainforest Cafe in Shaftesbury Avenue near Piccadilly Circus. Stunning animatronics and good food that's not toooooo expensive. For hot chocolate / coffee / cakes at a very reasonable price, go to the Crypt at St Martins in the Fields in Trafalgar Square. There's a Pizza Express in the Strand opposite Charing Cross station, but you can eat from a chain's menu anywhere - do something different!
At a slight tangent, if you were tempted to take a river cruise - don't bother. Take a Thames Clipper round trip. It's a fast river bus service using catamarans. You'll see the sights and, if you don't know what they are, buy a book for a fiver.
And don't get ripped off with a tourist bus, either. The route 15 still uses the old Routemaster and takes in Trafalgar Square, St Pauls Cathedral and plenty of other venues.
Keep your wallet and phone in an inside pocket in crowds (especially if you're checking a map), and enjoy yourselves!