Assuming you're flying into Heathrow, here is my idea of a leisurly walking/public transport trip that hits the major highlights: 10am - Take the Heathrow Express into Paddington Station - Buy a 1 day Tube/Bus travel card. - Walk due south to and around Hyde Park - Check out Buckingham Palace 12.30pm - Take the Piccadilly Line to Covent Garden - Grab lunch at a bistro in Covent Garden; look around shops 2.30pm - Walk to Leicester Square and down to Trafalgar Square; - Take the 15 bus to London Bridge; sit in the upper deck if possible. 4pm - Cross the bridge, leisurly walk west along the South Bank, checking out Millenium Bridge, and London Eye 5.30pm - Take the Bakerloo line from Waterloo back to Paddington Station - Take the Heathrow Express back to Heathrow Arrive back in Heathrow around 7pm