I recommend getting away from the tourist districts, into the neighborhoods, and just strolling around. Amsterdam is a lovely and generally safe city, and the old city is very photogenic. Find a canal and just walk along its edge; you'll take a U-shaped tour around some beautiful architecture and streets. My favorite area is northwest of the Centraal Station; I'm forgetting right now what the neighborhood is called, but it's filled with locals and few tourists.

Have fun!