I know Amsterdam pretty well.
Rent a bicycle. The City is designed for it and it will help you have a more Dutch experience. This is very important.
Check out www.iamsterdam.com
for what is going on and some good background, and www.timeout.com/amsterdam/
for the local scene and where to eat.
If the Reiksmuseum is still mostly closed, you can see the Dutch masters collection, basically the best of their collection, in an afternoon. There are many other museums, from tropical plunder to modern art, not to mention the Van Gogh museum.
If you are going to the Anne Frank huis, go in the afternoon closer to when it closes. The line will be much shorter.
Restaurant Nam Kee on the Zeedijk has amazing Chinese food and black bean oysters that they made a movie about. There are a lot of impostors on that street, so make sure it is the real Nam Kee. (Google the name with oysters and/or movie and note the address). Not particularly fancy or expensive.
Brasserie Harkema located on Nes, just off Dam Square is a decent place for dinner with a nice, hip atmosphere.
There is great food in Amsterdam. A lot of fusion and indonesian influence. You should definitely have a rice tafel at a nice indo restaurant. I like Sama Sebo, near PC Hoofstraat in the Museum quarter.
If you want American sports, try a Sky Sports cafe. The one on the Leidseplein is open very late and serves great late-night food.
Catch a show at Paradiso or Melkweg. Hotel Winston usually has decent live music.
If you like improv, try Boom Chicago, also on the Leidseplein.
Great shopping. The Kalverstraat is their shopping district. PC Hoofstraat is their Rodeo Drive.
I could go on and on, but you are only going to be there for four days. PM me if you have any questions.