What's the best time of day to go painting outdoors? In some ways, your own diurnal rhythms should dictate that for you. For example, I am at my most energetic in the mornings and can paint up a storm, but in the afternoons, even just lifting a brush can be a chore. Other painters I know do their best work in the evening hours.
But we should also listen to the sun. Because the sun is always in motion, the quality of sunlight varies constantly, and there are times when the quality of this light is better for painting than others. Photographers like to talk about the "golden hour" - the hour right after dawn and the hour right before sunset. Objects illuminated by sun at these times seem to be richer in color. Everything is awash with a golden light, and the world can look quite magical.
It's a great time to paint, if you are quick. Blink, and it is gone. For some reason, the sun always seems to move faster in the early morning and in the late evening. (It has to do with refraction, and with light bending as it passes through the lower, thicker and denser part of the atmosphere.) It doesn't take long after sunrise for the world to lose some of the magic and start looking dull. In the evening, of course, the light just keeps getting better and better - until, that is, the sun drops below the horizon.
The sun seems to move the slowest in the middle hours of the day. By then, the shadows are small and few, so there's not much contrast, and the color, being affected by the sun's cooler aspect at that time of day, is less rich. As you know, strong contrast and rich color are two essential tools in the outdoor painter's toolbox, and without them, it is difficult to build a good painting. We call this "flat lighting," when the sun is high and everything seems washed out.
There is a compromise, though. You can get reasonably good contrast and color between the "golden hour" and the middle of the day. After sunrise, I like to wait an hour or so until the sun has slowed down a bit and the shadows aren't changing so fast, and then I paint for two hours. In the afternoon (if I can lift a brush), I try to get out maybe three hours before sunset. I may paint all the way to sunset. It's always a risk when I do though. I make sure to get some good painting done before then and move to a much smaller canvas to capture the end of the day.
I remember a workshop I participated in several years ago. Students and instructors were all staying in common lodging and dining together. After dinner, just before sunset, one student, who'd had a bit too much to drink, became vocally enamoured of the gorgeous sunset and announced she simply had to paint it. The moment she finally managed to get her French easel erect, the sun and all of its beautiful color vanished. Some things just aren't meant to be painted but savored by the eye alone.
I created the above graphic to illustrate the concept. Feel free to share it with attribution!