From behind the Dom you follow a street to the right and go along the righthand of the canal that you will find. Watch for open doors and gates in little alleys on the righthand and enter them. You will find oasis of peace and quiet, not often without a lot of green inside them. Old buildings surrounding the will bring you back to medieval times.
I like to guide people around in Utrecht. Here Anya (Irina's sister) is enjoying the canals in the old citycentre).
Just a tip, there are a few operators who can give you a great time if you try one of those "party boats" you got to be with at least a few people, but then in summer you will have a great time on such a boat. I mean not the normal tour boats, but the boats the Dutch take when the celebrate something. Especially Utrecht is known for this kind of entertainment. Traveling by boat through the canals including beer, food and sometimes music.
See for example this website from the smulvaart: http://www.smulvaart.nl/English_Info_Smulvaart.html
But there are more of them.
Have a great time (best in spring/summer)
The Province of Utrecht (one of the 12 provinces we have) has a most wonderful STATENJACHT......a ship originally built in 1746!
For more INFO: see TRAVELOGUE "SPECIAL BEAUTY"......and enjoy!