Best lobster rolls are at Beach Plum.
http://www.tripadvisor.com/ShowUser...e_Beach_Plum-North_Hampton_New_Hampshire.html
They have a roadside shack on Route 1A in North Hampton across the street from a state beach. Parking can be a pain though. They also have a bigger place in US 1 about 3 1/2 miles from the Portsmouth Traffic Circle (not within walking distance of downtown). They are pricy; but, you get lot of lobster with that roll. Just don't try to drive and eat one of those big ones. I spent a hour cleaning off my steering wheel, dashboard, shift, etc. after picking one up in Portsmouth and then driving up to Portland.
Portsmouth is a great town. Plenty to do, eat, and drink. Typically a late 20's and 30's crowd both local and from Boston. If you happen to be there during a strong coastal storm (hurricanes, nor'easters), take a drive along Route 1A from Portsmouth down to Hampton beach. Nature puts on one heck of a show.