London: Go to museums--they're all free. The British Museum's collection is just about untouchable. They have the frigging Rosetta Stone and an Easter Island head. Tate Modern is awesome, and I assume the regular Tate is too. If you're there on a Sunday, go to Speaker's Corner in Hyde Park to walk around and hear people on their soapboxes yelling about whatever issues they want to. The entertaining ones draw big crowds and get into it with them. Paris: Père Lachaise is awesome. I skipped it my first couple of times and wished I hadn't. Louvre is amazing, but I preferred the Orsay. Quieter and more intimate. On the southeast side of the Eiffel Tower, there's a big park. Buy cheap champagne from the guys walking around and watch it light up at sundown.
Skip Versailles and spend more time in Paris. Versailles is a waste of time because they herd you through the place like you're cattle. Saint Chapelle is more ornate than Notre Dame https://en.wikipedia.org/wiki/Sainte-Chapelle Get some Moroccan food at Marche des enfants rouge. See if there is a cool exhibit at Au Palais de Tokyo. Try to get a reservation at Frenchie, Septime, David Toutain, or Verjus if you guys have a bigger budget for dinners. Pre fixe lunch courses are cheaper and pretty good.