The North of Amsterdam is the area north of the river IJ. It is residential district, and with about 86,000 inhabitants, it has the size of a medium-sized city (and it is growing at a rapid pace — three new neighborhoods are currently in construction). This district has remained well off the radar among tourists visiting Amsterdam, so amenities are not well-developed. It looks strikingly different from the city center, so get in with an open mind. Yet, there is more to see than you might think. The ferry to it in itself is a breeze, crossing the river IJ and showing the urban landscape of the North. Get off at the NDSM shipyard, that functioned as a shipyard as recently as the 1980s, but now boasts a lively art scene. Urban culture comes alive in its large skate park. Then patch up your bicycle, and ride it through the rural farmland in the east. The picturesque villages Ransdorp and Zunderdorp are favorites among the locals for their traditional Dutch farmhouses.
The north lies fairly isolated from the rest of Amsterdam, but luckily, there is a free GVB ferry from Central Station in the Old Center. Instead of just being a way to get in, the ferry ride is an attraction in itself. It gives a great view over the urban harbor-front, and shows the diversity of the north's residents. Large signs show when the next boat is departing, and when it does, expect masses of locals getting on with their bicycles. Getting on just before the boat leaves seems to have turned into a sport here. You can take off at different piers, the NDSM shipyard being the most notable. If you want to do some further exploring, be sure to bring a bicycle and a decent map.
Bike around the Waterland area. This is the beautiful polder landscape just north from the city. It includes nice small villages like Holysloot, Durgerdam and Ransdorp. The former Zuiderzee, which is nowadays a lake called Markermeer, is at the eastside of this area. You've got a gorgeous sight from the dyke that protects the land from flooding.