Another quiet neighborhood is located much closer to the city centre; located right across the river Ij from Centraal Station. Hundreds of years ago, the north of Amsterdam, or Amsterdam Noord, was not a pleasant place; full of outcasts, it was also the place for dumping bodies after bloody executions. Today, it is a quite residential area for many Amsterdammers. Green and full of bike paths, it's very different from the busy city centre and a pleasant place to visit by bike. If you're looking for a longer bike excursion, many routes to towns like Edam go through the North as well.
If an expensive canal cruise is not for you, go to the back of Centraal Station and take one of the public transport ferries crossing the River Ij to get to the north. The ferry is free, and you get an interesting view of the city from the water.