Is there really a best time of day for your session? Yes and no. Cameras will photograph at all hours of the day and night, and artificial lighting can certainly be used; but, if you ask my preference for your session time I'd say the evening hours. I prefer a natural light look for most of your senior portraits and the hour I am jumping for joy over the amazing light is exactly two hours before sunset. This is the time when the colors are most ideal coming straight out of camera. The hour before sunset is called the "golden hour" and rightly so. During that time the sun is lowest and gives off a beautiful warm, golden glow.
So what if you are only available for a session in the morning hours? Or over lunch hour? Don't sweat it. I most likely won't put you out there in the blazing sun where shadows are harshest and you're squinting just to try to look at the camera. During those times we find the perfect spots in open shade where you'll look fabulous.