I love Hill Country SNA, but it is definitely one of the more arid parks. The creek is small and difficult to get at from most of the campsites (West Verde Creek campground offers the easiest accessibility, but you need to look out for poison ivy en route to it.) You will have to hike a bit to access the creek, otherwise, other than of course the pond just before the park entrance (I don't know how much water's in there with our dry winter, but usually you end up driving through an inch or less of water from the pond as it slowly trickles across the roadway.)
There are Port-o-potties within walking distance from the campsites in West Verde Creek, though how close you will be depends on which site you get. It's actually closest to where you might park your vehicle. There are NO potable water spigots, so you'll need to bring water even for cleanup.
We're taking our 11-month-old on her first TENT camping trip in April, but we're sticking close to home--
Guadalupe River SP--and going with a park with lots of opportunities, including park playgrounds, a river, open fields for stargazing, some wildlife (albeit usually of the smallish variety--rabbits, racoon, etc.)