Should take an hour to get from Heathrow to Canary Warf on the tube...

£4 single

Madame Tussauds and Buck House are about a 45 min journey on the Tube from the hotel

And apparently there is a shopping center around Canary Warf http://www.londontown.com/LondonInfo...g_Centre/1768/

If you want to check for tube journeys... http://www.tfl.gov.uk/