I actually tend to forget about all these touristy places, but I've been to nearly all of them and live in London so you can PM me if you want help with planning.
My friends son came to stay with us from the middle of nowhere having never spent time in any cities and these are some of the things we did with him.
-Definitely take him on the tube in mental rush hour. You can always get off, so maybe plan a short journey but its an experience.
-Take him to places like Rainforest Cafe, Inamo, Benihana,
-Definitely see a show.
-Natural History Museum, Science Museum (Both in south ken/knightsbridge) and Tate Modern (which includes a walk along the Southbank and a look at Shakespeare's Globe Theatre and London Aquarium).
-Harrods, Liberty, Selfridges, Hamleys and then Ice Cream in The Parlour at Fortnum & Mason. This would mean Oxford Street, Regents Street, Piccadilly and Knightsbridge.
-Covent Garden, to see the entertainers and have a mooch around. Walked down to Leicester Square (we planned it so a premiere was just starting and he thought that was really wow seeing all the slebs).
-The palace, watch the changing of the guard, houses of parliament/big ben etc (maybe do this on a red bus)
-Go into the city and see the Gherkin and now the Shard. Friends son was amazed at all the suits buzzing around. Also around St Pauls or Bank of England.
-Other places are speakers corner, the parks, maybe some of the more exotic markets (petticoat lane is just along from Spitalfields, give you a taste of 'true' London). I tend to think Madame Tussauds is a waste of time, London Dungeon is ok but he might get a bit scared. Trafalgar Square.
-Depending on when you go the Olympic Park might have opened.