Finding the best time to train has a lot of scientific research to it. Some conflicting which doesn't help. However some of the most important things to think about are really common sense. For me personally I train when I'm not.. excuse the French. Fu@ked. Now for me that means when I haven't had a heavy night on the town (night out...hmmm what's that?) If I feel dehydrated because of the few beers the night before have really got to me or I just feel tired. Now personally I prefer to train in the mid afternoon just before the drove of teenagers amass and take up all the benches and start adding their pictures to Instagram bench pressing the bar. I need my space to be what it is.....space. I feel I can Get a lot more done in that time. Not just because there are fewer people there but I feel a sense of, I can get sh@t done.
Another great time to train of course is the morning. Now I'm sure you have read countless articles of why this is a good thing. It awakens you, It kickstarts your metabolism and generally you can workout and have the rest of the day to yourself. I totally agree on this. However, as science says, your muscles actually reaches the right temperature around early afternoon to late afternoon so for me training in the morning can feel a little sluggish. Perhaps this is why.
Training in the evening again for me Is a no go. The last thing I want to do is enter my gym when it is packed and every piece of equipment is taken. Its just a put off. Plus most of the classes are at that time so you get the extra traffic from that also. Not so good for the head space. Again when you are reaching the evening you have had a long day at work, your body is generally more tired at that point and going into a session can promote injuries. I would say one exception to this is hitting the bag. There is nothing greater than having a crappy day and hitting the heavy bag releasing all that stress knowing that when you get home you have to change the bedsheets (guys you can relate right)
So in a nutshell its down to what you and your body feel is right for you. Yes there is scientific evidence that early afternoon or early morning is optimal however in my experience of training clients for 20 years, it's what works best for you.