I'll second @Smithy's suggestions. If they're Fuyu persimmons, they'll be sweet even while they are still a bit crisp. I love them in salads or just cut up. I also like the idea of a pickle.
Here's a beautiful persimmon salad with pomegranate made by @FrogPrincesse. A more ordinary salad I made a while back with persimmon, broccoli, curly red lettuce, pickled cranberries, toasted almonds and blue cheese. And a more recent one from @ninagluck with endive, persimmon, lardo, hazelnuts and cream cheese
Here's an older Persimmon thread with some ideas.