I have seen the courts near the little red light house.
There are also some hard courts in Riverside park near 119th. Away from the river.
It is hard to explain unlesss you paly tennis, but I think that playing on clay is just nicer. The ball bounches differently and takes differently to spin and pace. It is easier on the legs too. The downside to the clay courts at 96th Street is that you are required to sweep the courts when you finish and then clean the lines.

There are also har-tru clay courts in Central Park. You don't have to sweep there. But they are always crowded and the ball doesn't bounch the same as in Riverside at 96th. They do dry off faster after it rains.