Good meeting spot. Speaking of waterfountain, you can find more interesting ones in Rhodes for sure but it's nice in any case.
Nice fountain located close to the port where you book day trips to different islands.The birds like to drink here.
A square on the waterfront which is basically an open space/park of sorts. You can sit there and people watch and is also a nice place to take pictures of the harbor as well as the nearby waterfront landscape.