I have been camping at Hermit Island for my entire life. Every year we have an annual camping trip there with friends and family. I believe this is the best primitive camping experience you can have.
Some info that may be helpful. Campsites do not have any electricity, there is no water at the sites, but most water faucets are a short walk. No radios or music allowed in the campground. No cell service (you may be able to get a little at the office).
We love the quiet the campground offers due to the no excessive noise. I have noticed campground security drive around somewhat regularly at night, even stopping and shutting their lights off periodically to see if anyone is making a ruckus.
Most campsites have a lot of privacy. You're neighbors are not right on top of you like most campgrounds I've been to. The sites are a good size, at times being able to fit 3 maybe 4 tents in a pinch, though they do say 2 adults and 2 children. 1 vehicle per site with additional paid parking off site from 3rd parties.
I've been to other campgrounds with beaches, but I love Hermit's beaches, they are very long with plenty of room for everyone. There is one beach open to the public and the others for campers only.
The store has basic necessities as well as selling live lobsters and clams that they will even cook up for you and give you a time to come back to pick them up. Across from the store is the Kelp Shed which has some tables, arcade games, pool tables, and a small snack shack for stuff like burgers, pizza, sandwiches, ice cream, etc.
As someone who drives 3+ hours to camp here, I love the feeling of "being in the middle of nowhere with no cell service" it really brings back the good old days of camping, you have to find your own fun.
The hiking trails are fantastic, they range from short to long. All relatively easy. They all have great sights, especially the one along the rocky coast. You can even hike to a private beach!
If I lived closer, I would camp at Hermit's Island all the time. It is by far my favorite campground.