If you like museums, I would definitely recommend paying a visit to the Musée D'Orsay in Paris. Personally, I prefer it to the massive and overwhelming Louvre, particularly since I am a fan of impressionist art.
In addition to this, the gardens at the Musée Rodin in the seventh arrodissment (district) are a beautiful, relaxing place to take a walk. Several sculptures of Auguste Rodin - including the fabled 'Thinker' - are displayed in the garden. Skip the museum unless you are a big fan of Rodin's work. The small museum also houses a few of VanGogh's more obscure works.
I would defintely not miss the Rue Cher, a market street where many local Parisians shop. It is a great place to pick up a few things to take home. Don't miss the tiny crêperie about half way down the street - It has been written about in the Washington Post and the LA Times. Rue Cher is located in the seventh arrodissement!
Another great place to visit is the Pere Lachaise cemetary on the east side of the city. This is a remarkable place to visit; many famous people - French and otherwise - are buried here. You can pay your respects to Jim Morrison, Oscar Wilde, Chopin, and a host of other influential people.
Of course you will probably want to visit some of the more 'mainstream' attractions, including the Louvre and the Eiffel Tower. It is best to get to the museums fairly early in the day, before most of the tourists arrive. Also avoid museums on Sunday, as admission is free and the crowds are large. Many of the museums are closed on Monday. I recommend visiting the Eiffel tower shortly before twilight and staying up there as the city grows dark - it is really beautiful.
The Arc de Triumphe is interesting to see, but I don't recommend going to the top - unless you are older you will have to use the stairs, which are taxing to climb and, trust me, the view doesn't pay off.
I would also visit some of the department stores tucked behind the Opéra Garnier, in the ninth arrodissement. On top of being interesting to shop in, many have observation areas on the roof which provide a nice view of the city.
And, on top of all of this, I recommend using the métro in Paris - it is the most efficient way to get around the city. Buy a carnét of ten tickets and you'll be off to explore the most beautiful city in the world.
Amsterdam is a great city as well. I haven't spent a lot of time there, but I would say that I found the VanGogh museum to be enjoyable. I also enjoyed the canal tour, which is a great way to get an overview of the city if you are pressed for time. If you haven't booked a hotel yet, consider staying at the Bôtel - a floating hotel near Amsterdam Centraal - the rail station. If you take the Thalys train (go first class) to Paris, it will depart from there. It is centrally located and looks to be an interesting place.
On top of this, be advised that in Amsterdam a café is where you go to enjoy a cup of famous Dutch coffee and the Coffee shop is where you go to enjoy Amsterdam's other specialty! Anyway, I hope you have a wonderful trip. IMO, you are visiting two of the worlds most beautiful cities - enjoy!