| Dayton, MT

Like the cold, clear waters of Flathead Lake, mystique surrounds Cromwell Island. It overlooks the legendary Wild Horse Island, where Salish and Kootenai historically swam their horses to keep them safe from rival tribes. With 348 acres and nearly three miles of shoreline, Cromwell is the largest private island in freshwater west of the Mississippi River that is under a single ownership. The island was purchased in the late 1980s by Robert M. Lee, a renowned automobile and antique arms collector, explorer, author, and conservationist. Before his death in 2016, Mr. Lee and his wife, Anne, partially completed construction on homes including 45,000 square feet of living space. Even in its unfinished state, ''The Villa'' has a magnitude of presence reminiscent of Versailles.