I went to the trinity site a couple of years ago and it was pretty cool. Like everyone else said there is a monument at ground zero, and the debris, but they also have a few other small exhibits on the missile range related to the testing. One of which is a little house where they built the plutonium core. On the bus to and from the site they also played a little film telling you about the development of the bomb and the scientists involved.
If you are going, I would also suggest after you leave to visit the Old Owl Bar in San Antonio, NM. Apparently they were one of the nearest restaurants at the time of the testing, and as a result used to serve many of the scientists from the site. They have a really good burger, and they make a green chili relish that is pretty good to put on it. ^