I don't think that's a sufficient condition. I too am from a New England town that was incorporated more than 200 years ago. But it doesn't have the density or the amenities that you're describing. (I wish that it did!)
Yes, we have more Art Museums than anything we need in our daily lives. What I like about it is the lack of access to high consumption. What is bad is that the large chain stores killed the local businesses and then realized the market is too small to really care. Jbullock35 how about some clues about your town so we can try to guess.
Yeah that's fair, it's never just one thing and not all old towns are going to be like that, but it's pretty common in at least Massachusetts, particularly if you're in proximity to a larger town. It's also a much denser state in general than Vermont/Maine/New Hampshire, from what I remember growing up there.