There was a recent thread asking about a location a block away that should help answer your question. In the forum search bar, type in "Mexico Piedras safe" and you'll find it. Keep in mind that the replies were addressed to someone from a U.S. suburb who doesn't speak Spanish and isn't familiar with South America.
There are lots of restaurants on Chile, as you head towards Defensa. Also some good ones on Venezuela, on the other side of the Av. 9 de Julio (around San Jose).
As for the safety of streets at night, that would vary from place to place, as it does in every city. I feel fine on the streets of San Telmo at almost any hour, but personally, as a woman on my own, I wouldn't be relaxed walking around Mexico and Tacuarí at night.