Last time I went was in 2010 and I took my board, although I didn't skate all of these spots as I was out with family (par the fountain one in Protaras which I got to skate). I wouldn't bother with the parks as the recent ones don't look up to par. Cyprus seems to have a lot of untapped spots around whenever I've seen locals do edits, although I guess it's better than it being blown out like Barca. Anyways;
Outside Larnaca Municipal Art Gallery there's a a cool fountain spot, you can pop down and skate the ledges inside or outside. Right next to it there's a little statue that has a manny/tiny ledge combo that looks pretty fun. There's lots of flatground and the spot looks pretty cool at night.
There's a rad plaza spot that seems to be one of the 'main' spots people visit when they do trips to Cyprus that's in Nicosia. As me and a few friends were meant to go two years ago I finally found out where this was by scouring Google Maps ahah. This is right next to a church called Panagia Palouriotissa. This has tons of ledges here.
There's a cool hip pyramid type setup in Ayia Napa, right next to the Thalassa museum. Although the surface doesn't seem to be amazing. I wouldn't check this out if you're in the party central times although, with COVID being around that's probably not even a worry..
On the main road next to Capo Bay in Protaras there's the fountain ledge that's been seen in a lot of footy over the years, that's pretty fun to skate. They kind of curve around.
I remember seeing some cool bits down Ayia Napa Harbour that seemed skated, lots of little steps and ledges...I saw some Israeli guys if I'm right, skating these. I cannot pin point it nor find them on Google Maps when I last looked. Possibly been changed in the past ten years? I dunno.
There are a row of these businesses that have a driveway type gap, there's one constantly skated in edits but I cannot find that one at all. It's on the main road on the way into Larnaca if I'm not mistaken.
That's all I can think of on top of my head. Take a look at some edits because there's lots of cool hits within the streets there as well.
I hope to get back out there at some point.