I've no idea how they will celebrate National Watermelon Day in the US. Just eat a lot of it, I suppose, and perhaps some poor soul will have to dress up in a puffy green outfit.
If you'd just like to get into the eating part, here are a few ideas to help you celebrate:
Like most fruits (except banana*) watermelon works really well in salads. It's especially good with salty cheese like haloumi or feta. I often just chuck a load of diced watermelon into a bowl with olives, crumbled feta, basil and some balsamic glaze for a quick and easy supper.
If you've a bit more time, Josh Katz's salad makes a wonderful starter or light main.