Dog Canyon is an easy and interesting hike near Big Bend National Park's northern entrance. You do have to put in some work before it gets good, however, as the first mile and a half of the 2-mile hike is across wide open and flat creosote desert. After this the trail drops into a dry wash that you will follow downstream for a short distance into the canyon. You will be looking at this canyon from a distance for the entire hike, but is actually farther away than you probably anticipate.
Once you finally reach it, you'll be dwarfed by huge limestone walls on either side. Dog Canyon is a sheer cut through the Santiago Mountains, where water has somehow found a weakness and over the ages has carved right through to the other side. The gap is much taller than it is wide: There is only about 100 feet between the walls, but there is more than 300 feet overhead. There are many boulders, pockets, and caves along the side of the canyon that kids will love to explore. Look closely for fossils embedded in the rocks as well.
The canyon even has historical significance. A sign at the trailhead explains the story of the U.S. Army's "Camel Corps" experiment of the 1850s. Back when the West was truly wild, the government sought a better way to transport people and supplies across the barren deserts. They thought, naturally, of camels. A fleet of these "ships of the desert" were imported from Africa, and local handlers were hired to come over with them. Army officers led a caravan through the Big Bend region, which seemed the perfect proving ground. They passed through Dog Canyon to cross the Santiago Mountains, then continued south to make a loop around the Chisos Mountains. The camels were able to handle the terrain and travel days between water sources with no problem. The experiment was actually a great success; however, the advent of the Civil War distracted from further camel operations, and soon after railroads moving westward negated the need for beasts of burden to travel long distances in the desert.
If Dog Canyon doesn't fill your day, you can take on the longer and more strenuous hike to Devil's Den, an offshoot of the Dog Canyon Trail that travels to a narrower and more adventurous canyon.