One tip is that the buses are great for short trips and much easier than getting crushed by the crowds on the tube.
Another is to avoid restaurants with "steakhouse" in the name! If the weather is good just go to Marks and Spencer and get some sandwiches and drinks etc and have picnic lunches outside.
I'm returning to London with my five year old soon, and I'm going to take him to the Changing of the Guard, Science and Natural History Museums, Tate Modern, St. Paul's, boat trip down the Thames, Tower of London, Tower Bridge, Hamley's, Selfridges (he loves shopping!) and a trip to one of the parks. If we have time we are going to go to Canary Wharf and go on the driverless trains, and maybe also across to Greenwich. And to Borough Market for some great sausages!
I was thinking of taking him on the Eye, but it takes quite a while for it to do one rotation, and if he started freaking out it would not be pleasant for the other passengers!