Definitely grab an Oyster Card to ride London's Tube. Not only will it cost less per ride, but there's a daily cap. Meaning you can travel as much as you like, but will only be charged for a certain number of journeys, the rest are free.
Enjoyed all the (free) museums but looking for something more adrenaline-pumping? Ride whitewater rapids at the Lee Valley White Water Centre, built for the games in 2012.