Visit the various exhibits at the El Paso Museum of Archaeology for your fill of historical information if you want to see something fascinating and enjoy some free things to do El Paso. It is understandable why history buffs and interested people frequent this museum, which houses fossils and relics dating back 14,000 years, north of the Franklin Mountains. It also boasts 15 acres of land that are dotted with more than 250 different native desert plant kinds ideal for those who enjoy hiking on nature trails.