The Mummy Mtn loop was always my favorite ride in Phx, but it's complicated. There are some short hills, but everything is rideable on a fixed gear. ABC (Arizona Bicycle Club) rides it regularly, and might have more info on their website:

http://www.azbikeclub.com/

The canals have low traffic, but are boring. Traffic is pretty sketchy in Phx, and "share the road" is lost to many SUV/pickup drivers, so be careful. The downtown area is usually pretty dead, so the streets are probably clear most of the time. Usually when I'm down there I stick to the mtb. The trails are better than the roads.