I would suggest those places i've been to on our london holiday last month, you can try going for a bateaux lunch cruise at thames river - best way to explore london
also try the london eye ride - splendid view specially at night although a bit scary for me, lol.... you can check out harrods, buckingham palace, westminster abbey,
westminster square, st. paul's cathedral/millenium bridge, london tower and london tower bridge, and of course shop at oxford highstreet
You can also check houses of parliament and big ben, and 7 downing st. - the prime minister's official residence,
picadilly circus, leicester square and trafalgar square and also check out the west end theatre and all the other theatre's there,
they got so many interesting shows to choose from
and of course the museums and galleries
Also don't forget the chinatown and enjoy an authentic chinese food - yummy
there's a lot of other interesting places we went to, but i didn't get the name of those....there's quite a lot to explore there really
and i would suggest to explore london both by day and night
a very interesting place indeed
Of course, visit the windsor castle and have a tour inside - which i highly recommend
I'm sure you'll have fun exploring london as much as i did