The foothills of Virginia’s Blue Ridge Mountains, south and west of Washington, D.C., are a playground for the city’s old guard, their horses, and their beagles. With its laird-of-the-manor grandeur, no place evokes the regional esprit like Keswick Hall. In a stately Tuscan-style structure originally built in 1912, its 48 guest rooms are decorated with a mix of hunt-club prints, canopy beds, polished armoires, and Chippendale chairs. There are hints of fun: one room holds a framed collection of Best in Show ribbons that somebody’s poodle won. Fossett’s, the swag-festooned restaurant, serves some of Virginia’s most compelling food—quail with chanterelles, rockfish with mussels and fava beans—with bottles from up-and-coming local wineries: King Family Vineyards, Blenheim Vineyards, and Kluge Estate.