All of the shelters at the park are reserved for the day I was hoping to host a birthday party. Are there grassy areas near the splash pad and playground where I can set up my own tents and tables?

On top of the hill you might be able to fit a table and one tent. Otherwise the hill with the most grassy area is on a slope so it would be hard to put tables and tents up. There is an area by the park that isn't covered but is shaded that you could probably do that. But it's not immediately next to the splash park but I think it would work great.

No