Huh. Well I don't normally do these meetup things but this is close enough that I suppose I may as well swing by.
If the park you're thinking of is the one I'm thinking of, then it's a nice enough place to hang out. Overgrown enough that it's almost wild, but not quite. Pretty big. Only issue I can think of is that the restrooms are, as far as I know, not intended to be used and always locked. There's plenty of secluded trees, though, so for a bunch of gentlemen of dorfy persuasion it's entirely probable that no problem will arise.
Shasta caverns (I'm assuming that's the caves you mean, there's no others of significance particularly near Redding as far as I'm aware) are nice enough for folks who haven't seen northwestern caves before. But at a meetup in the northwest, I don't reckon there's too many people to whom that applies. It's not as impressive as some of the other caves around.
I don't know where you're thinking of camping, so I can't comment on that.