Not all the quirky parts of town are historical, but a lot of them are. In my book, you'll find references to the Choate Bridge, and the Choate Bridge Pub.
The bridge, adjacent to the busy downtown intersection and for more than a hundred years one of the only ways to travel south, is the oldest stone arch bridge in North America.

The Choate Bridge pub is on the corner next to the bridge.

My protagonist walks and runs on Labor in Vain Road. She finds someone near death from a drug overdose just over the Labor in Vain Creek Bridge. According to legend, probably true, when the Ipswich River silted up, locals would try to row up the river, but at about the point when they encountered the creek, they realized they were "laboring in vain."
Lauren walks in the historic cemetery.

The next book in the series already features Crane Beach and the Crane mansion, a stately residence that sits atop a hill overlooking the beach. It involves a real-life conflict between the Feoffees of Little Neck and the local School Committee. Stay tuned!
What is your favorite locale-as-character?