Cherry Springs
I write this with the caveat that we did not actually spend the night in Cherry Springs State Park. I favor campsites with privacy in the woods, even if they lack the amenities of public campsites. That being said, we did spend the evening on the public viewing field falling asleep under the stars. Sleeping on the field all night isn't actually allowed, so we camped at Little Lyman Vista, which we found on a map of the area. The whole area is very gorgeous and I HIGHLY recommend going for stargazing. If you have flexibility with your dates, try to go on a new moon or a meteor shower!