The Oudegracht (Old Canal) is really impossible to miss during your visit to Utrecht. On the one hand because of its well known name, on the other hand because it runs throughout the entire city center.
As such, you encounter among others the Winkel van Sinkel, the city hall and the many wharf cellars that are common in Utrecht. The various wharves at the waterfront are also the place where you find terraces when the sun is out. A great place for a bite to eat and a drink down by the water.
The oldest bridge and a national heritage monument as well is the Maartensbrug (Bridge of Maarten) across the Oudegracht, which you cross when you walk from the city center to the Domtoren. A great way to explore the city is by taking a boat tour over the Oudegracht, walking past its many bridges and wharves. Another fun option is to explore the canals in Utrecht by canoe.