Nationally, the average for new construction is about $100. In New England, it's more like $200/square foot, and definitely higher in urban areas or upscale suburbs. Remember that even at $200/square foot, the quality of finish details will likely not be to your standards. Shortcuts like hollow-core doors, vinyl windows and low-grade light fixtures are built into the lower cost per square foot price. If you want something like you see in a remodeling magazine, figure on $300-$400 per square foot and up. Aspects of home building that were once standard are now considered luxury so prepare yourself to pay more than you expected or be willing to compromise. Since you are in Hingham, this may not be an issue.
One reason that the price per square foot of additions is so high is because, unlike building a house from scratch where the cost is spread out over a much larger footprint, an addition tends to require a lot of work for a relatively small finished product. Again, remember that you will get what you pay for, so go with the most reputable builder you can find (and add 30% to the estimate and double the timeframe)