Perhaps the village's central shopping and dining area, and the bascule bridge that spans the Mystic River between Mystic's Groton and Stonington sides, were not big tourist attractions in the 1980s. After all, that was before Mystic Pizza (not filmed in Mystic) became a nostalgic favorite. Or perhaps I was just a clueless, day-dreaming child who didn't pay attention. (I was.)
These days, however, the historic districts anchored by West and East Main Streets, and the twisty quasi-grid of hills that branch off from them, are almost always full of people. People lining up for tours, people sitting outside drinking coffee, people watching that famous bridge raise up, as the line of cars and pedestrians waits to cross, then watching it lower again.
If you, like childhood me, are of the belief that the Seaport and Aquarium are all Mystic has to offer - or if you, like grown-up me, can't afford the crazy admission fees - I encourage you to go explore the downtown area. It's not exactly off the beaten path; in fact it's pretty bustling. (Get there early for easier parking, and don't miss the side-streets with their enviable historic homes and fewer tourists.) But I'm sure there are many visitors who pass through the village without even thinking to venture beyond the familiar old school field trip spots.