Badajoz makes a good base for exploring Extremadura and the western edge of Portugal. Mérida, less than an hour east, has some of the finest Roman ruins in Spain — the theatre, the amphitheatre and the aqueduct of Los Milagros. Cáceres, a UNESCO World Heritage city, is about an hour and a half north and rewards a slow wander through its almost untouched medieval centre.
Across the Portuguese border, Elvas is just 15 km away — another UNESCO site, with the largest dry-moat bastioned fortress in the world and the spectacular 16th-century Amoreira Aqueduct. The whole town is walkable from the bus station; bring your passport.
For nature, the Cornalvo Natural Park east of the city has Roman-era reservoirs, dehesa oak woodland and good birdlife. Further afield, the dolmens of Valencia de Alcántara and the megalithic landscape around La Serena give a sense of the deep prehistory of the region.