Clinton County is a rural county in south-central Kentucky along the Cumberland River. Known for affordable land prices, minimal zoning restrictions, and strong agricultural use, Clinton County is popular with homesteaders and off-grid buyers. County seat: Albany. Lyon County, located in Western Kentucky with Eddyville as its seat and a population near 8,210, is known for its recreational opportunities around Lake Barkley and Kentucky Lake, presenting land buyers with prime locations for building a waterside retreat or a homestead with ample outdoor leisure.