Cindy's in Yarmouth has exactly what you're looking for. Thin, almost intermittent batter, onions are nearly caramelized. Excellent deal there for lobster rolls too.
Estes in South Harpswell ME are very good. A few weeks ago we had nice puffy battered rings at the Red Hill Dari in Center Harbor, NH. We are overdue for a visit to the Ice House in Newcastle NH. Can't remember what their onion rings are like.