Tate Modern
It's really very good
If you don't like modern art, you probably won't be at the Tate Gallery. It's a shame as you will miss one of the most interesting places in London. The old central Bankside has been turned into a museum and it's amazing. Visit, as I did, during your vacation to see the turbine project time in the lobby. The area surrounding the sun has people lying on the ground just looking at the top. The museums are full of some of the most wonderful works of modern art that are both illuminating and delicious and lots of fun. I advise you to go in the middle of the day to avoid the hordes of tourists.
Also, don't miss the restaurant. The 7th floor café has incredible views of St Paul's and the Thames. The food is a bit expensive (but not too much) and there is a nice surprise! The icing on the cake is that the Tate Modern (as in most London museums) is free. I can't recommend the museum highly enough. Next door is the Globe Theatre, which is also worth a visit.