As in the area of land now within the modern borders of the country of Mexico? Or do you mean their own empire and territory?

If you mean the city itself: Tenochtitlan is located in the center of where Mexico now is (and its sister city Tlatelolco right next to it). Those two cities were the only one in the middle of the lake.

The "Aztec Empire" was the "Empire of the triple Alliance" (in Nahuatl Excan Tlatoloyan, more literally "tribunal of the three Chairs", incorporating Tenochtitlan, Tlacopan and Texcoco, three cities around the bassin). The people inhabiting Tenochtitlan/tlatelolco called themselves Mexica.

(sources for that: Art History 380 at UBC, taught by Marvin Cohodas, about Art History in the Aztec Empire).