Despite the very kind words of others, there are a number of people on (and especially off) the Forum who have a greater knowledge of the Dales than I. However, I am always happy to proffer mi two-pennorth and encourage people to sample the delights of this little bit of paradise that is now 'home'.
Contours offers a "Three Dales" walk that seems to be in the area that a number of you recommended. http://www.contours.co.uk/walking-holidays/fact-files/three-dales-way-IT3DW.php. They've offered to modify it to three nights and two walking days. What would you say to this: Arrive Burnsall, first night. Walk to Kettlewell, second night. Walk to Malham Tarn, third night. And then....how in heck do we get back to London from there by public transportation?? That would be about eleven miles a day; I could probably squeeze another three or four miles out of my daughter, if there is a side trip or particular feature that you think is particularly worthwhile.
In fairness, that looks a good itinerary. The walk along the Dales Way from Burnsall to Linton Falls, along the River Wharfe, is a delightful introduction and the Grassington to Kettlewell section a pleasant walk across some slightly higher ground and passing by one of the areas well known limestone features - Coniston Pie.
Second day includes a favourite track of mine - the Monk's Way - but I usually do it the other way round. And the last part of the walk across the limestone pavement and then down by Malham Cove is a highlight on its own.
Getting back from Malham - there is a bus service from Malham to Skipton -
http://www.dalesbus.org/ runs 4 times a day taking about 40 minutes. At Skipton there are frequent trains running into Leeds (about 35 minutes journey time) for the connection to the East Coast Main Line traind running to London Kings Cross.
Side trips - on the stretch from Grassongton to Kettlewell, just before the Coniston Pie a track leads down to the valley through a narrow limestone gorge known as Coniston Dib. Pleasant walk down and back.
One not to miss - from Malham the short walk to Janet's Fosse and then Gordale Scar. It is the start of the last day of the Contour walk, but Gordale Scar is woth a visit on its own. Could easily be done at the end of the second days walking before hitting the fleshpots of Malham for your last night of revelry.
I'll post up a couple of other suggestions tomorrow should you want to have an alternative to the Contour trip.