If there's one word to describe Austin, Texas, it's quirky—but in a good way. Shopkeepers exude an independent spirit. Over 200 live music venues suit a myriad of tastes. The list of top-ranking restaurants includes slick boîtes and hole-in-the-wall shacks. Austin is the capital of Republican Texas, and yet the city itself is very liberal. And alongside the new residential towers, shopping districts, and strips of chic nightspots downtown, there are places that remind you of Austin's long history. Among them is The Driskill Hotel.

Since opening in 1886, The Driskill has been much more than a place to spend the night. The hotel was named after the cattle baron who founded the hotel (and according to legend, lost it in a poker game). Lyndon B. Johnson awaited presidential election...