Re: What is the location of the US' first morning light?

I'm not certain I completely understand what you are asking. Your sense of the geometry of the interface between night and day may have been influenced by maps showing some sort of complex curve, such as this one at The Night Sky Live. But the transition only looks complex because of the distortions you get when you project the spherical Earth onto a flat map. At any time, half the Earth is lit, and half unlit. These halves are separated by a great circle, which is the spherical equivalent of a straight line. (It isn't a perfect great circle, because the Sun isn't a point source infinitely far from the Earth, but it is close enough that we can treat it as perfect for most purposes.)

On the equinoxes, when the Sun is above the equator, this great circle runs through the poles, and the line separating night from day is parallel to lines of longitude. At any other time (with the solstices being the extremes) the great circle is tipped away from the poles, so your latitude along any particular longitude affects the time of sunrise or sunset.

If the U.S. had rectangular boundaries, by which I assume you mean the horizontal edges were parallel to lines of latitude and the vertical edges to lines of longitude, the entire East Coast would experience sunrise at the same time on the equinoxes. At any other time only one point would be the first. From the March equinox to the September equinox, the northeast corner would see the sunrise first. During the other half of the year, the southeast corner would see it first. You would never have a case where sunrise occurred simultaneously at just two points. In practice, it would be rare for the actual moment of the equinox to coincide with sunrise or sunset, so many years would pass between times that an entire coastline experienced sunrise or sunset at exactly the same time.

Because the actual boundaries of the U.S. are complex, the time of sunrise is also complex. It can be calculated exactly for any given geographic coordinate and date, but there is no way to identify a pair of locations with the same sunrise time without testing all the points along the eastern coastline.

There are many Internet sites that will calculate the times of sunrise and sunset, such as the United States Naval Observatory. I didn't find a good online reference detailing the math behind these calculations. The classic reference is Astronomical Algorithms, by Jean Meeus. I highly recommend this book if you are interested in such things.