Syracuse is worth more than an hour or two I think. .. Technically you could do what you want to do - it's not a very long drive from CTA airport to Syracuse, probably about 45 minutes ( Finding parking near the old town can take a bit longer though ! - There's quite a bit along the ramparts on the East side , but it can be busy in peak season especially if you're arriving later ) ..

Riposto is then back past Catania in the other direction .. so probably more like 90 minutes from Syracuse, especially if there's evening traffic going through Catania .. so unless you're looking for a very late dinner I would think you won't have a lot of time in Syracuse with your plan .. I would say better to do it another day as a full day trip from Riposto where you can get there in the morning , have more time to look around and get a nice lunch

Can't help you on the beach club question I'm afraid !