In London, the big ones are the Tower of London and Westminster Abbey. The changing of the guard is pretty boring, so unless you feel you have to see it, I would skip. The rest depends on your own preferences, like Rajah said. If you like shopping, Harrods is great. The British Museum is awesome, if you're into that. Wagamama is a restaurant chain whose first location is on Streatham Street a few blocks away. For art, there's the National Museum in Trafalgar Square.
In Paris, the Eiffel Tower, the Louvre, Notre Dame and the Arc de Triomphe are really "must-dos". I also loved the Musee D'Orsay and the Sacre Coeur in Montmartre (the view from the steps of the basilica is fantastic; I did that at night). I wish I had seen Sainte Chapelle, which is near Notre Dame and has stunning glass windows, but it was too late in the day for me to be able to view it.
For both cities, the Underground and the Metro are great ways to get around.