The Amsterdam Historic Museum, a fascinating portrait of the history of this more than 700 year old city.
It's in a side alley of the Kalverstraat (Amsterdam's best known pedestrian shopping street).
Also look at the flower market on the Singel.
By the way, I agree that the Rijksmuseum must not be missed. I was there in 2006, and in spite of the restauration, they had put together a very good overview of Dutch art, culminating in Rembrandt's Night Watch.
I am not much of a 'Van Gogh person' myself, but the museum is good if you like that art form.