We highly recommend crossing the river to the tiny Mexican town of Boquillas. Have lunch, buy some souvenirs and even stay the night. This charming village relies on Big Bend visitors to survive. Bring your passport and cash, they do not accept credit cards in town. The crossing to Boquillas is inside the National Park, check here for current hours and keep in mind there are often closures. After arriving at the crossing you'll be rowed across the river and then have the option to walk or ride a burro into town.
Quirky little artist town located on the way from El Paso to Terlingua with cute shops, places to eat, and art installations.