Six weeks if fine for a super saver ticket but if you know when you are going book now.
If the weather is nice I would suggest a morning walking seeing all the main sights -Big Ben, Buckingham Palace, a couple of parks. My dds just loved jumping on and of the tube a genrally getting around. Also a wander along the south bank looking at the various street artists etc..
If the weather isn't so good I would say science museum (basement is great for young children).