Start with the London Eye and the combined bus and boat tour - very tourist orientated but will give them bearings, etc.
Art - all the usual recommended places plus Saatchi, White Cube, etc for contemporary. Look out for really unique one offs like the Soane Museum in Lincoln's Inn Fields, the Handel Museum in Brook Street, etc, Wren's City of London churches,
Shopping - no idea really but try New and Old Bond Street, South Molton Lane, etc for the expensive stuff - Picadilly, Regents Street and west (not east) Oxford Street for one offs like Burlington Arcade and department stores, including Fortnum and Mason, Selfridges and Liberty's - Harrods, Peter Jones, Covent Garden, Kings Road, Soho, 1 New Change (next to St. Paul's Cathedral), Borough Market etc, etc - and then there's the new 'malls', Westfield in Shepherds Bush and in Stratford City (new Olympic park),
Food - too many to list.
Misc - Somerset House or Broadgate for ice skating (like but not like the Rockefeller Centre), National Theatre and/or The Royal Court, Royal Opera House and/or English National Theatre...........................................
http://www.timeout.com/london/christmasBuy a good guide, do some of the tourist stuff but try some of the less well known bits as well.
