What's the best time of the day to workout?

Morning - Best potential for building muscle because testosterone is critical in protein synthesis and for rebuilding muscle fiber damaged in weight training. There is also greatermental focus, which may allow for greater mind-muscle connection and greater efficiency of muscle work done.

Afternoon - Best potential for breaking plateaus by employing muscle shocking techniques because pain threshold is highest and the limits of the body might be able to be pushed further than usual.

Evening - Best potential for strongest performance. This is the time of day when the body is in peak condition for physical activity.

Besides the purely physical observations about circadian rhythm that have been mentioned, there are other considerations that one might take into account when deciding the best time of day to weight train:

Morning: Is fat loss or fat storage prevention a goal? Morning exercise may help in reaching this goal partly due to higher than normal testosterone. It also helps that your body has not had much food to process yet, and may turn to fat for energy instead.
Exercise has shown to increase serotonin levels. Low serotonin has been shown to be related to depression. Exercising in the morning could possibly help elevate mood slightly for the rest of the day. It should be noted, however, that significant changes in overall mood can take a long time to occur, and will happen as a result of a general increase in serotonin.By doing a workout in the morning, it will be out of the way, out of mind. 
Afternoon:Good balance between all the issues discussed in both morning and night sections.

Evening: If working out too late, this can affect you're body's natural time of slowing things down for sleep. Working out increases ability to absorb nutrients on a cellular level. If adequate nutritionis not in place after a workout, the body might soon be left hanging for an eight hour fast while you sleep.
Is the gym open late?