Whether you want to or not, biking the dikes outside the city is an experience not to be missed! Marty and I did get a bit lost and ended up with only about a hour to actually bike on the dikes, but riding around Amsterdam-Noord opened our eyes to a part of Amsterdam I would love to explore more. The dike is first lined with quaint little homes on one side and a gentle river inlet on the other before fields open up after the homes and the river turns to open ocean. If you persevere you can take the dikes from village to village and enjoy the more country side of Dutch culture.
There is a free ferry behind Central Station, where you can rent bikes, to cross the Amstel River. The bike rental places will give maps of the biking routes and directions to the ferry.