Recommend one of the hop on/hop off bus tours, we did the Big Red Bus Company, if you book online in advance it's cheaper. You also get a river cruise as part of the tour.
Westminster Abbey is stunning, thought it was worth the entrance fee, so much history. St Pauls Cathedral also.....we ended up in here during a service.
Tower of London is worth seeing. The just wander past Parliament down past Downing St etc.
If you are interested in WW2, then I recommend Churchill's War Rooms - the underground rooms where he spent much of the war, that's in Whitehall....also the Imperial War Museum. There is also a new attraction called The Blitz, supposed to recreate what that was like.....but DW wasn't bothered about seeing it!
Definately recommend going to Harrods just for the food halls.....DW couldn't believe I was taking her to see food halls....until she saw it and insists on taking everyone there now!