London: The Tate, Museum of London, The Tower of London, Camden Locke Market, stroll through Hyde Park and visit the Hampstead Heath, Highgate Cemetery, The Sir John C Ritblatt Gallery in the British Library, stroll along the Thames, Westminster Abbey, The War Rooms, Changing of the Guard at the Pallie,theatre, theatre, theatre, every night by getting tix at the Half Price booth in Leicester Square. I'd even try a London walk, www.walks.com.
Paris: Rodin Museum, Notre Dame, Louvre, night cruise on the River, watching the sunset and the Effiel Tower lighting up by sitting in the park by the Tower, Invallides, Picasso Museum, Museum de Orsay, Pompidou Center, Chartes Cathedral, the skeletons of Paris, ie. the crypts below AND ignoring the Champs de Elysees,
IN both cities visit the open air markets and have a picnic if weather is good.
These are my must sees, whether or not they do anything for you depends are your preferences.