It's funny you should post this as we have reservations for Pinnacles for this upcoming weekend and I have been second guessing whether we should go or not. When we booked in May, I assumed the pool would be back open, albeit perhaps with reservations or social distancing restrictions. With no pool and no nearby natural water for cooling off, I'm concerned we're going to broil. It doesn't help that when I looked at the site I picked on Google street view (after the fact of course), there's very little shade. And then we were notified of the "no fire" restrictions, so no hot dogs over the fire or s'more roasting.
The lure for us is a Junior Ranger badge for my son, who has been steadily building his collection, and hiking the High Peaks -- Condor Gulch loop. Since there's no vehicle traffic allowed past the campground, we're planning to bike to the trailhead (which is a plus for us, being able to bike on traffic-free roads), but that's going to make for a long hot day. It seems that if you're not able to bike or hike to the major trailheads, there's very little to do there other than the one trail along the road going west from the campground. I think we're still going to go and if it's too hot, we'll just call an audible and go home Saturday, although it's a long drive for us from Sacramento for a single overnight.
Unfortunately, the pickings are very slim for any alternatives, especially if you're looking at weekends. You may want to look for private campgrounds, county campgrounds, or check HipCamp for possibilities. Or look for campgrounds with lots of first-come, first-served sites and try to make it there early in the day. How far are you willing to drive?