Off the top of my head...
6 places you can only get to by boat.
6 corners (Speaker's corner, Staples corner, Highbury corner etc).
6 places still associated with a trade (Smithfield, Billingsgate, Soho, Inns of court etc).
6 places that were really important to you as a child.
6 infamous places (Rillington place etc)
6 places that have been transformed recently (the wharves into flats, covent garden into a tourist trap etc)
6 of those private roads with gates and "No Entry" (they make me really cross...)
6 places you are likely to get hassle for taking pictures (Airport, MOD, Embassies, LOTS of places these days and a good way to make a comment on it).
6 friday night tribes (Warterloo commuters, the central mosque, West end party people etc.,)
6 London squares
The same place / street / view at six times of day and night or over six days
6 of those little black cab cafe huts (becoming rare these days).
6 wild flowers growing in the cracks in the pavement.
OK - head empty now
Best wishes
Monty