caterpillar-girl: if it's your first time in London, try the hop-on-hop-off tour so you get a glimpse of what London has to offer. The hop-on-hop-off tour takes you around the city and passes by any city highlights / tourist spots. If anything catches your fancy, you can go back to it later.
If you like museums, you may want to drop by the British Museum, Victoria and Albert Museum or Sloan Museum.
Of course the famous London Bridge is there to catch your breath.
If you like shops and cutting-edge art, tour around the eclectic London's East End. Most artists and creative Londoners go there to shop.
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PARIS
Try to explore Montmarte in Paris. Renoir, the famous impressionist artist, lived there. Van Gogh, Monet and Degas all lived nearby (Butte) as well as Picasso. There are also old vineyards there that still produce wine. If you like outdoor cafes and restaurant, check out Place de Tetres. If you also want a view of Paris rooftops (who doesn't?), don't forget to go to Sacre Coeur. While in Montmarte, see the famous Renoir work at Moulin La LaGette. Nearby is the famous cafe (forgot the name) where Amelie was filmed (perhaps you should ask some locals about this once you're there). Nearby that cafe is Moulin Rouge.
If you like to see Paris in its magnificent glory, dine in along Avenue des Champs-Elysees (the world's most beautiful boulevard).
Places best seen at night: Place de la Concorde Square, Place Vendome, Opera, Champs-Elysees, Arc de Triomphe, Trocadero, Invalides, Notre Dame Cathedral and Place du Chatelet.
Of course seeing Eiffel Tower is a given but if you have more time, take the Siene River Cruise. If you have to see Mona Lisa, The Louvre awaits you.
If you're staying in France for more than a day, you may want to set aside a day trip to Versailles, Mont Saint Michel and spend a night at Chateau du Bouceel in Normandy. My cousin's bf owns that beautiful chateau.
While in Normady, check the local tour operator for the Normandy D-Day trip and check out some of the beautiful beaches there.
There are a lot to see in Paris and you'll see more if you plan your day carefully. End your stay by dining at a French restaurant, with French wine and pastries. Paris is haven for foodies!
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Personally, if I were you, I'd stick to London and Paris. Maybe I'll give London 3 days and the rest in France since there are so much to see. Whenever we go on trips, we usually spend 10 days per city to maximize the experience and sometimes, that's not even enough!
I hope you enjoy your London and Paris trips and hope you enjoy my suggestions.