I stayed at Hotel del Faro which is in the Faro district. It was a quiet area: Residential, but a beach right across the road. A few grocery stores within walking distance, safe, and the bus that runs along the coast passes by there (plus various others that will get you into the city within 30 minutes). There were quieter beaches away from the touristy La Perla. Plus, the aquarium was also within walking distance (about ten minutes on foot).
Hotel del Faro is run by two Russian immigrants who are absolutely lovely and were very welcoming (asking what we wanted for breakfast, letting us pick the rooms we wanted, fresh breaky) and it was very clean. For the price, it's well worth it.
Further down the road is a pizza place run by another couple of Russians that had the most delicious pizza I had, had in a while. Reasonably priced, friendly, and the daughter was absolutely precious.
Also, go to Pancho Villa! It was decent Mexican food by Argentinean standards and they had spicy, spicy sauce.
