My husband and I have lived in Texas—Dallas and Houston—for many years, but had never been to the Panhandle. February can be quite cold there, but we went, hoping for less crowds and not-so-low temperatures. 
We were lucky on both accounts. Narrow ribbon-like country roads, big skies, and broad landscapes characterize the Texas Panhandle Plains. Much of the land is filled with cattle, goats, farms, oil pumpjacks and wind turbines. There are plenty of breweries here. This region is what many non-Texans associate with Texas. Lubbock, Abilene, San Angelo, Amarillo and Wichita Falls fall within the Panhandle region. All of these cities are worth a look.
Some of the highlights of the area are:
Palo Duro Canyon
We stayed in a cabin overlooking Palo Duro State Park, the second largest canyon in the United States. We stayed in the more secluded Doves Rest Cabins (the Goodnight Cabin) with unobstructed views into the canyon (see a room with a view). You can explore this beautiful canyon on foot, horse, jeep or by car. Due to a winter storm a few days before, all the hiking trails were closed during our stay, but the drive through the park was stunning. The large ravine includes 800-foot cliffs with spectacular formations of multicolored layers of rock and steep mesas. 
One of the most striking is Lighthouse Rock. During the summer months you can experience the Texas Outdoor Musical. Set in the canyon in an amphitheater, the musical is about the history of Texas. Palo Duro Canyon is a setting for the filming of Indiana Jones and the Last Crusade!
Cap Rock Canyon
This canyon is located along the eastern edge of Llano Estacado in Brisco County, about a hundred miles southeast of Amarillo. The elements of wind and water have created the dramatic canyon where bison wander the plains. There are 90 miles of trails here which can be explored by foot, horse or bike. The views from the car are remarkable too. Camping is available. You can take a virtual tour on the Texas Parks & Wildlife website under the Interactive Park Trails and Trailway Map.
Amarillo
When you think of Texas cities, Dallas, Houston, Austin or San Antonio come to mind. Amarillo can hold its own amongst these Texas powerhouses. It is the perfect blend of Texas cowboy and urban sophistication.
Landmarks in this area include the Cadillac Ranch and a preserved section of Route 66, which features unique restaurants and shopping. There are plenty of arts organizations here: the Amarillo Symphony, Lone Star Ballet, the Amarillo Opera, the Museum of Art and Botanical Gardens. The Quarter Horse Hall of Fame applauds and preserves the history of this noble racehorse
The Big Texan Steak Ranch & Brewery is a great place to stop. Before reaching the restaurant, you will walk past a shooting gallery, a gift shop, two stuffed bears, a mannequin on the electric chair, and a buffalo head. The walls of the restaurant are lined with more mounted heads of the area’s wildlife. They offer a free dinner if you can eat in one sitting their 72-ounce steak along with the side dishes of shrimp cocktail, baked potato, salad with roll and butter. We asked our server if anybody is able to do that, and she said all the time! It is so much fun for adults and kids alike—a fun, and kitschy western style tourist adventure (see my review on Trip Advisor).
Comanche
On the drive back to Houston, we spent two nights in Comanche, Texas. The city of something less than 5,000 people has a typically beautiful historic main street and town square. We stayed in the Jean-Marie Suites, a unique second floor apartment in an early 20th Century building, with a ballroom in the back. It is beautifully renovated, full of antiques and has all of the comforts of today. It is available through Airbnb.