The castle we see today is the result of an 1830s restoration. You have to walk across a small bridge that spans the moat to get inside for a visit to Catania’s Museo Civico. The admission is free, and on the ground floor you can see archaeological pieces that were mostly collected by the Prince of Biscari in the 19th century. From here you can also exit the castle for a walk around its base for a true sense of the building's monumentality. Back inside, there is a second floor to visit that displays Sicilian religious paintings, as well as a small gallery that is dedicated to rotating exhibits.
Catania is surprisingly (or as some might say, embarassingly) short on museums for a city of its cultural richness and size, but at least this museum is attempting to fill that gap. Although I do hope that the city’s archaeological museum will reopen someday, here you’ll spend a pleasant hour or so viewing a small museum in an impressive Norman castle, without spending a penny.