The average high temperature in the Phoenix, Arizona area is 66-67 degrees in December-January, just a few degrees cooler than your target. It is often in the 70's (for example today at noon it is currently 72, with an expected high of 77). There is also very little rain; most days are sunny. Tucson has similar weather in December-January, with a slightly higher chance of rain.
As far as biking, it depends on whether you want relatively flat trails or mountain biking, as you didn't say.
The Scottsdale Green Belt is a paved trail several miles in length that begins just north of Shea Boulevard and ends in Tempe. There are only a few places on the trail that require crossing a street, as there are lots of tunnels that pass below busy streets.
For mountain biking, I recommend South Mountain in Phoenix which is the largest city park in the world. There are more than 10 different trails in South Mountain ranging from 1 mile in length to 14 miles (58 miles total). Difficulty ranges from moderate to difficult. There are several other mountains in the area.