If your budget is running low or you just want to wander off the beaten path then jump on one of the ferries crossing the IJ channel behind central station. You will get a nice view of the city and enjoy a (small) nautical experience. The line going to the old NDSM ship warf covers the longest distance, it is one of the nicest.
The ferries connect the center of the city with the northern part of town that is cut off by the huge IJ channel.
All ferries but the Java island one are free of charge.