I highly recommend the Sience museum. It's free, as is the Natural History Museum. Harrods is not far from there and you can get lunch in one of their less formal restaurants. Not cheap, but not exorbitant either. Harrods itself is worth a look, especially the food halls. Not much fun for kids, but the toy section isn't bad.
Check and see if the funfair is still operating in Leicester square. Very well lit up at night and so is Picadilly Circus - an easy walk from Covent Garden. There is also the London Transport Museum in Covent Garden. Covent garden is buzzing at night with no shortage of eateries. You will also find street performers drawing big crouds around the Piazza.
See a show! I recommend Joseph for the kids with (a short walk away from where you are staying on the Strand). Booking at short notice might be difficult, but there are kiosks around that sell last minute tickets.
The Hard Rock Cafe on the corner of Hyde Park is an experience, but you often have a long wait. To get round this they give out pagers so you can go off. Green Park is opposite and Buckinham Palace is a five minute walk across this park.
Right near the London Eye, you have the London Aquarium (under the old GLC building)
The London Dungeon used to be a great attraction, on the South side of London Bridge. Also near here is HMS Belfast which you can go on.
There are loads of things to do, but I would check everything out online and have a good look at Google Earth before you travel to get your bearings and avoid dissapointment.
Have a great break!