Outside of Mexico City are the Aztec ruins of Teotihuacan. Many day tours from the city are available, but to avoid souvenir stops and big groups, visit Teotihuacan without a tour. It's easy with public transportation!
Despite being skeptical about walking tours, I actully really enjoyed this free walking tour of Mexico City, run by Estacion Mexico. They took us to hidden corners of CDMX and we found places even Mexicans didn't know about!