Can't figure out when the best time to run is? Try all three of these times to understand why each could be beneficial, and figure out which one is best for you. Having a good run makes you run again.
In the Morning: Body temperature is at its lowest. Some people take well to this, and are able to perform more efficiently and more comfortably in the early hours of the morning. Some people also say they perform better in the morning because they have a "clear head. " In my opinion, I would rather wake my body up (see above) and back it with the science. Early morning runs are actually the worst for your body from a scientific standpoint because your bodily functions are not awake, so you'll spend half the run doing that.
Mid-morning/afternoon: My absolute favorite time to run! Your physical functions have woken up and you've only had to deal with the good kind of stress in the morning: that morning productivity high. In the morning we all work well. We're riding the wake up high, and loving life. I ride off the momentum of accomplishing things in the morning on my runs. So mid-day is best for me physically and mentally. Also, your lung performance and body temperature are both at an optimal level of efficiency. If you have a good high-protein breakfast, your body will also have had time to get it's energy levels up. There are virtually no negatives associated with running in the afternoon.
In the Evening/Night: A lot of runners run better in the evening because of the psychology behind it. Think about it; in the morning, we're all feeling like "wow, this is awful." So, in my opinion it can be better to run later in the day, because you have had time to gather yourself, and perhaps even discover a reason to run. It's better to wake up your body and brain, after you wake up, to give yourself a mental and physical warmup.
You also run better during the latter part of the day, because you have already had hours of fluctuation in the performance of your body's functions. By fluctuation in body functions, I mean the rhythmic patterns of brain sending signals to your body to do things like eat, walk and think. Now, since your body has had hours of carrying these functions out, you are more geared up and primed to run. In other works, you are ready to neurologically and physically operate more efficiently.