The Paphos Archaeological Park and Tombs of the Kings are two great outdoor sites in Paphos that are definitely worth visiting if you're there. They're sizable park areas for walking around by the coast and checking out the ruins up close.
You can generally walk all over and even inside a lot of it including the tombs. The Archaeological Park has many preserved mosaics with a building built over them along with some that were left outside. I've seen such mosaics in museums but it's interesting to imagine the ancient houses over them in their original locations by the sea.
I like to imagine the people and their lives back then and what might have motivated them to spend the time and effort to construct all of this. It's interesting to think about how humanity has changed but also remained the same. We saw the ruins of nice palaces by the sea and then returned to our nice resort by the sea. We sipped wine looking out at the Mediterranean much like those people long ago must have done.
ruins of a castle
Tombs of the Kings
the view from our temporary palace by the sea