I suppose Tilted Barn in Exeter, RI would qualify. Though I'm not sure if you can be considered a small town if you're a 40 minute drive from every person who lives in the state (which is like 1.1 million people).
OK, a brewery that meets the small town criterion: Wayward Lane. As already mentioned in this thread: "Wayward Lane Brewing, from Schoharie, NY, which has a population of maybe a thousand people." I was there this past Saturday attending the annual (but first for Wayward Lane) Logjammin' Lager Beer Festival. Spoiler alert: I will be constructing a 'trip report' for this event and posting it in the upcoming NBW thread discussing new beers (for me). Cheers!