Please don't rule out the museums. Just be selective in what you see. (All of the major national museums are free so you won't lose out if you only spend a short time in each one).
In particular, your youngsters will love the Pattern Pod at the Science Museum:
http://www.sciencemuseum.org.uk/visitmuseum/ga lleries/pattern_pod.aspx
Spend a short time exploring the highlights of the rest of the museum and then head to the Natural History Museum, which is just around the corner. Go straight to the far end of the Dinosaur's gallery, where you'll find the moving (and roaring) dinosaurs. Kids just love them.
(South Kensington tube station serves both museums).
If the weather's good, you could call in at the courtyard of Somerset House. Mum and Dad can enjoy a drink while the kids have fun dodging between jets of water that shoot up from the ground:
http://www.somersethouse.org.uk/whats_on/107.a sp
(Temple station is the nearest to Somerset House).
A lovely way to see the main sites is from the river. If you buy One Day Travelcards, you'll get a third off all scheduled riverboat services. I recommend the trip between Tower Pier (served by Tower Hill underground station) and Westminster Pier (served by Westminster station or you can just walk over the bridge from the Eye). It only takes about 40 minutes (so the kids won't have time to get bored) but you get to see lots of interesting places.
http://www.tfl.gov.uk/assets/downloads/river-t imetable-leisure.pdf
Chris