I've been to all three several times. I'm in Agrigento right now, on my way to Piazza Armerina for the Villa Romana del Casale.
Segesta is amazing, the site of the temple from the road, rather isolated in the countryside, is spectacular. It is unfinished. There is a little bus that will also take you to the theatre nearby.
The temples at Agrigento are less mysterious, but more extensive. You can see the sea from the temple area. There are two archeological zones and a good museum.
Villa Romana del Casale has the interior decoration, although from a later period, and is constantly under restoration; some areas may be closed, but there is lots to see, including watching the work in progress (just don't interrupt with questions, the restorers are very focused).
I wish I could help you decide. I have to admit that I lean toward Segesta and Villa Romana.
Note that winter hours will be shorter.