I'm now a suburban chick but love going back to the big city (even more now I know I can leave all the traffic & sirens behind)
My fav 2 things are a walk along the southbank, taking in all the street artists, views etc The Tate Modern is good but usually massive queues in half term. Or a day spent in Hyde park/Kensington Gardens. The kids would love the Peter Pan play area in Kensington gardens. Both weather dependent but both free.
if you fancy the london eye, check out the website first as you can usually get the flight plus a meal deal at a nearby restuarent chain for just a few quid more.
As your there all week, get yourself an oyster card for travelling as it works out cheaper than buying a travel card every day.
The london aquariam is meant to be fantastic but pricey.
If they have been learning about Florence Nightingale at school, there is a a FN museum at St Thomas hospital nr the southbank which is open to the public in the afternoons. Or the great fire of london monument outside monument station (surprisingly) My Grandad took us their umpteen times as kids "to learn" but really it was coz we were lazy oaths who spent all day watching tv & playing on our game boys. Its just a tall tower containing hundreds of steps up to a viewing platform.
The BGM of childhood is ok but only worth a couple of hours visit if that, you could make more of a day of it if you cross over the rd and walk up the high street to brick lane market (although good 20/30 min walk with kids) and there is also the Geffry musueam? not sure on the spelling, in that neck of the woods where they have a house & each room is decorated to a different decade.
The bus routes have probably changed by now but the no 43, 12 & 10 buses were good for site seeing - have a look on the tfl website.
Have a great trip