Was tenochtitlan a good site for a city?

the legend says that the Aztecs where searching for an eagle eating a snake on top of a nopal in a small island in the middle of a lake (those prophecies where more specific) so they just placed the city there, but the real reason was because it was near water. So, the Aztecs used the water for transportation and drinks. Also, it was surrounded by mountains and that gave them protection.