I got the ascensore balbi up the hill (entrance on via balbi, next to the big pharmacy on the corner) which was free. The castle is almost directly in front as you come out of the station and I had a lovely wander around the grounds of the castle (free). The views across the city are great from up there. Instead of going in the castle I had a drink and some focaccia from the castle cafe and sat outside enjoying the views instead. A lovely (and cheap!) way to spend an hour.

Got there using the Ascensore Balbi which was quirky and free! On leaving the ascensore, the entrance to the castle is practically across the street. A slight incline to walk up to the entrance which provides some lovely views across the city. There is a cafe where you can enjoy a coffee or similar. If you want to visit the castle and museum, then the entrance is €6pp. They provided us with an English guide book which was useful as we walked through the one way system. We were there on a Friday and it was busy with school groups but it didn't interfere too much with our visit. Downside, just one toilet for each genre off the main entrance hall. We took our time, enjoyed the views and the quirky exhibits before having a hot chocolate in the cafe and we spent 1hr 45mins there. Was a pleasant visit while we were in port on a day visit on a cruise ship.