In Agrigento there is a public bus just near the station that takes you to the temples.
The stop is to the right with the station behind you.
We found the unmarked stop and just waited till a bus came along and asked that driver what to do.
It was the right bus and we paid him, so bring change.
Returning to the station, the stop at Agrigento was marked, but the bus we got on took the long, but scenic! route back to the station.
In Syracuse, we couldn’t find, and never saw, a single public bus in five days.
We did ask and got vague replies.
We just walked to the archeological park from Ortigia and back.
It took about 40 minutes, but we walked slowly as it was hot.
We went between Palermo and Syracuse by InterBus.
Easy website, bought tickets in advance .
It takes 3 hours, with a stop for 20 minutes for bathroom and snacks at a services stop.
This was all in May 2023.