If you want to find beaches in Argentina, go to Mar del Plata. This is the hot spot to hang out. 
We found the least expensive way to travel is by bus from Buenos Aires; there are dozens leaving every day. The coach buses are very comfortable and a pleasure to travel in, but since the trip is only about 5 hours, you can go economy if you want to save some money.
We wanted to be close to the beach, and found a gem of a hotel in a safe, quiet area that overlooked the beach. The Amerian was better quality than many of the places we stayed in Argentina, at economical rates. The room was clean and in good repair and the staff provided excellent service. They even spoke English! We were able to walk to the shopping areas and parks, but took a taxi to the casino or to go sightseeing. The taxi costs very little, and we had a lot of fun with one driver who took it upon himself to point out many of the sights and acted like a tour guide rather than a driver.
We arrived in Mar del Plata in the late November, just before the local crowds, but the ocean was still cool for swimming and the surf was rough. However, the surfers loved it and we saw lots of young people on boards trying to catch the waves.
As for the food, local fare was good, but be aware that paper napkins are a rarity. Most often customers will get a small waxy type of tissue which does not have much absorbency if you are eating pizza!
Shopping is fun, especially at the Genoa sweater shops where the beautiful knits are irresistible! There are also lots of local merchants who set up booths along the busy pedestrian walks or by the parks.
This is a small city (population about .5 million) compared to many tourist spots, so we found it quite easy to find our way around with a good map, and it has many sites that are worth visiting or photographing. This city has lots to offer, and is still a bargain compared to many destination resorts.