I have an idea- The Botanical Garden!
They're free on Saturday mornings (before noon). The rest of the time, kids under 12 are free and adults are $3 resident/$6 nonresident.
We go there pretty often, my daughter (almost 3) loves the children's garden (though I think the little train is still broken, that was her favorite thing in the children's garden
), the bird garden, feeding the huge koi, and just running around.
We could have a sort of potluck picnic lunch, maybe? There are a lot of open spaces to sit. I know they don't mind people going off the path and onto the grass, but I'm not 100% sure about whether or not its okay to lay out blankets in the grass and have get-togethers. We'll probably go there tomorrow, so I'll ask.
Before 5pm is good for us during the week, and before 3:30pm on Saturdays.