Nice surprise
Nice spot right near downtown Monterey. I live in the area, but when friends or family come into town, we usually stay here. Sites are first come, first serve, so get there early if you want to camp on a weekend in the summer. Dog friendly, and there is a big lawn area they can run on off leash, as well as a small playground for kids. There is access to a few hiking trails as well.
One thing to note is that in the dry season they do not allow campfires. If that's a deal breaker for you, call ahead of time and double check whether or not they ate allowed when you want to camp.
Overall, it's a fun, cheap alternative to the overpriced hotels in Monterey and only about a 10 minute drive from downtown.