9 hours is plenty of time to get in and out of the city.

The quickest way (and most expensive) is the Heathrow Express to Paddington. Give yourself 30 mins for the journey (15 on the train plus time to walk through endless passages to the train and off the train).

Alternatives are heathrow connect which is cheaper and slower (not recommended for your short stopover) or the Picadilly tube line. This is good if you want to go somewhere on the Pic line as it's probably just as quick as the HEX after to take into account the changing of tube lines and a fraction of the price.

On the Picadilly line you can go to South Kensington (for museums), Knightsbridge (for Harrods), green park (for Buckingham palace), Leicester Square, Picadilly or Covent Garden.

Heathrow to green park is about 45 mins

Give yourself plenty of time to get back into heathrow though just in case there are delays

Enjoy

Jon