Have at least two hours for this park. I spent four hours because the Ear of Dionysius surprised us with a wonderful acoustics and we wished to play with sounds more.

The Roman amphitheatre is located closer to the entrance. I guess, to preserve it better, they don't let you walk inside of it.
The Greek amphitheatre, a craved in stone ancient theater is located further away and open for everybody to walk its stairs. Once you walk around it there is a wonderfull view of the city. It has an open semicircular form and it looks great from different points of view. Make sure to walk around at the top and go to the stage.

The Orsi Museum is located a couple of blocks from the entrance to the park. Leave about three hours for the museum if you are interested to take a look at everything.   The entrance to the archeological museum is also included in the price. If you are a more thorough visitor and want to read about each artifact, you will need more then four hours. This museum has a large collection and, I believe, it is the most significant in Sicily.