There is some great fishing in the Hingham area. Previously mentioned World's End is a good start. You could pay the $4.50 fee or get an annual pass which I recommend, not only because it is a good thing to support, but they really have a ton of great properties in Massachusetts. Some of these places on the North Shore are great fishihg spots as well. Check out http://www.thetrustees.org.
Another good spot to fish from shore is Stoddard's Neck on Route 3A. This is good during the spring when the herring are running in the Back River. Also try the Lincoln Sailing Club pier at the Route 3A rotary. I have caught many stripers from there on flies, especially in the shallows inbetween the piers. During the summer when the water temp heats up, head to Cohasset and fish off the rocks. There is some great fishing from the rocks at Black Rock Beach. If you want to get some more info on some of the places I mentioned and many other shore spots in the area, pick up a copy of Jack Gartside's Fly Fishing Boston Harbor. Another good book is Fly Fishing Boston by Terry Tessein. Good Luck!