We went to Sandy Hook a couple times. The cons are that it's close to the beach, clean and some sites with a built canopy, which make them a good shelter from rain. The best part is that the camping site is within walking distance to some wild beach with lots of fun for kids. The biking trail is good, pretty much flat, and separated from the car lanes, so very safe, even for small kids. Staff are nice and generally helpful.
However, there are some drawbacks. First is the parking is really limited. It's not a drive-in camping site. You have to park outside, and take your stuff to the site. It's not far, only within a minute or two of walking, but if you have a lot of stuff, it might not be the best idea. Secondly the parking is very limited, only 16 parking spots for 20 tent sites, plus a lot visitors park there for the day. The overflow parking is about 5 minutes walk down to the south. The major problem is coming up recently. There are some bars across the bay, playing super loud music well into the mid-night. On one night, it played all the way to 4AM from 10PM from the previous night. The base can be heard throughout the site. Several people even called the police, and clearly didn't help much. A lot of people complaining about it, but it seems nobody can pinpoint where it's from. So if you're a light sleeper, don't expect a quiet night especially on weekends.