Dont forget to factor in the increase immigration times and the extra time fo security checks on the outbound leg. Should be about 45mins each way to london by the tube from heathrow, should have about 6 hours in town.
http://journeyplanner.tfl.gov.uk for times.
I've not got a bus tour running this year ;) but a tourist bus trip would get you around pretty much all the main sights. Failing that start at tower bridge, then onto St Pauls for St Pauls Cathedral, then onto the tube again and westminster for pics of the house of parliament and big ben. That way you start out at the furthest part and work your way back.