Um....do you want free or paid? Natural History Museum (v obvious sorry!)
Battersea Power Station? You could get an uber boat there if it works from where you are. There's a little pop-up funfair atm (old fashioned rides, think big wheel is like £8 - good views!). There's a boardwalk and the landscaping is fun to walk around (or scooter!), there's a big shopping centre (might tempt the jaded teen) then you could walk into the park where there's a little zoo, nice place to run around.
If you find yourself in Covent Garden (likely with a teen), head to the top of the Royal Opera House, up the escalator. They have some nice ballet costumes and ephemera on display in the bar area and you can go out on to the balcony and look down at Covent Garden. Good for a free loo stop too.
Would you ever head out to Canary Wharf? You can take the DLR between stations and ... your kids are probably a bit old for this, but it's kind of fun to sit at the front and pretend you are driving and it feels like a monorail up high. Then you could decamp at Canary Wharf where my kids always feel like they have landed in America or somesuch. Good place to wander around with the landscaping and by the water etc (get lost in the 7th circle of hell that is the shopping centre!) I am sure there are things for kids to do there.
Boat to Greenwich/cable car/park? (I'm just thinking of geographical locations you might not have done to death)
Oh, I know you said your 11 year old isn't into art, but the Young Artists Summer Show at the RA might appeal as it's all art by kids. She might be inspired! You could do a 'guess the age' of the artist! It's free, (closed Mondays) and then you have Green Park opposite or oooh, you could go across to Fortnums and their new Biscuit Emporium which has fun buttons to press and lots of lovely treats to look at. Pop into Waterstones also to the kids book section, or Hatchards. That's what I would do with an 11 year old actually. Really feel like a tourist in my own city!