What are the exact directions or tube stops that get you from the Hearthrow airport to the London Visitors hotel?
Where is the hotel? What directions did you get from the hotel? What is the nearest Tube station?
If you combine this: http://www.londonvisitorshotel.com/hotel-connections-central-london-hotels-discount-book-online.php with the tube map here: http://www.tfl.gov.uk/gettingaround/14091.aspx you will see that you take the Piccadilly line to Hammersmith. Then you walk, or you change to Hammersmith & City/Circle to Shepherd's Bush, and walk.
You would want to take the Piccadilly Line to Earls Court (which would be the 12th stop from airport terminals 1, 2, or 3 if leaving from terminals 4 or 5 it would be the 13th stop) at Earl's Court change to the District Line take the District Line to Kensington (Olympia) tube station (the 1st stop). Kensington (Olympia) is the closest tube station to your hotel.
When i lived there the Olympia station was only open when they had something on at Olympia. has that changed? Usually that spur and station are not operating