El Paso, directly across the Rio Grande, is the obvious day trip — or the base from which you day-trip into Juárez. The El Paso Museum of Art, the Chamizal National Memorial (which commemorates the 1963 border treaty between Mexico and the US), and the Franklin Mountains State Park are all worth a visit.
Farther afield, Copper Canyon (Barranca del Cobre) in the Sierra Madre Occidental is one of northern Mexico's great sights — a system of canyons deeper and wider than the Grand Canyon. It is a long day trip from Juárez; most people overnight at Creel or Divisadero after the scenic Chepe train ride from Chihuahua city. Chihuahua itself, the state capital, is three to four hours south on Highway 45 and has an excellent museum of the Revolution housed in Pancho Villa's former home.