Hi,
It really depends on your budget as to where to stay. There is a heathrow express that goes to paddington I think. Thre will be plenty of hotels etc round there and it's quite central with good transport links to everywhere including kings cross which I believe the eurostar goes from now.
Paddington is near the river, a place called little venice is nearby and you could walk down the river, (or get bus) to london zoo and also regents park is close. In town you could go down to Westminster on the tube, where you have houses of parliment, big ben, and across the river over the bridge is the london aquarium and london eye. plus a few museums are very close walk along the river there. If you head to leiscester square on the tube, you have all the cinemas where the premiers take place, then next to it is picadilly circus which then leads onto regent street where you'll find hamleys (big masive famous toy store) and further down crosses oxford street for shopping.
Really depends what you son is into and how much you want to do,
Also at paddington your close to portobellow market in notting hill, which is on saturdays, and then hyde park isnt far from there, (there's a big playground if you enter in at kensington gardens end of the park.) Best thing to do is get hold of a tube map and A-Z to see the places I'VE Mentioned and see how easy it is to walk / bus around. also, there are open top tours of london you could do that pick up all around london.
Most of the places I've mentioned you can probably find on line so can find out how much etc. in terms of transport, head over to http://journeyplanner.tfl.gov.uk/
or http://www.tfl.gov.uk/ to find out prices, as tube / travelcars alone will be a good few £.
hope that helps!
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