Driving west out of Austin toward Fredericksburg, the road narrows to one-lane blacktop, and the edges of the city’s suburbs gradually give way to a different kind of Texas, one of ranches, old wooden churches, farm stands and wineries.

This is the Texas Hill Country, a 31,000-square-mile area of rocky karst hills considered the threshold between the Southeast and the Southwest. As the center of the state’s wine tourism, and with a more temperate climate than the nearby cities, the region has lured visitors for generations, whether for the hiking or the tempranillo wine or to just get away from it all.

Figuring out where exactly the Texas Hill Country begins and ends is a task best left to local songwriting legends like Willie Nelson and Lucinda Williams, but over a recent weekend, with Ms. Williams’s gravelly twang on the car speaker, I cruised the region’s back roads to see what was new, particularly in terms of accommodations.