Feel free to redirect me if this has been answered before, but is there any way to tell when this website is at it's peak of activity?

About 1 to 2 minutes on any given post.

around 4 o'clock.

It does not matter that much, in my opinion.
You might get a bit more views when it's daytime in the US, with mild peaks in the morning / lunch / evening.
But it's not big enough to base your upload schedule around.