I think it really comes down to experience and the method you have developed through the years. If you need large swings 8:30 to 10:00 cdt will normally provide. If you have learned how to trade chop 10:00 to 1:00 cdt will produce 1.00 pts in ES and almost always 1:00 to close can acheive 1.50pt plus moves. I seldom ever take trades though after 2:35cdt, unless I am trying to get to breakeven on the day.
I have broken down my backtesting into these three different time segments. Each require different risk and targets generally based on these segments. The only change I can make are based on last six ranges of each five minute bar. if they are expanding beyond normal, then targets are expanded but not risk.
Usually, the first hour of day session will provide the high or low of the day to be made. I like using the ATR of last several day sessions to help figure out where the market might go, this will allow me to possible move the "chop" segment either way.
So the "BEST" times to trade are really based on your method and not time of the day.