I went to Peddocks after making stops at Grape and Bumpkin from Hingham harbor. The boat ride takes about an hour, including the stops in between. Many of the people I saw on the boat were camping on one of the islands. I was only there for the day and took the 3pm ferry back (you can get on at 1:40pm, but won't get back to Hingham until after the 3pm Peddocks stop). There is a great brochure explaining all the structures on Peddocks. One of rangers even explained some of the film of Shutter Island and which buildings were featured (along with CGI to add additional structures). To get to the less rocky beach, you need to walk a small path from one side of the island to the other. There are some privately owned cottages on that beach.
There is some free parking in the Hingham lot...you just need to get a pass to put in your car.