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Just wandering around is a good call, but if you want to wander in a slightly more informed way you can join a walking tour. It's nominally free, although you'll end up tipping your guide a bit. Keep an eye out for various markets, which you can revisit on your own.
The Rijksmuseum is quite impressive and an audioguide can help you do the "greatest hits". I understand the Van Gogh museum is also very good and on my list for next time.
The ferry across the river can take you to NDSM , which is part of a regenerated/ing industrial neighbourhood with lots of artists in residence and you can go to Pilek or Noorderlicht for that sunset beer.
I'm pondering a trip to Amsterdam, where should I stay that's convenient for the touristy stuff?
Also, what touristy stuff is there?