Get to the beach early to beat the crowds, and once you are there do not be offended by the Argentinian tradition of kicking sand on your blanket and face :)
Tango shows at Teatro Colón are fantastic and at only 15 pesos for Buenos Aires dance companies, they are a steal.
Enjoy mate, the very bitter and caffeinated but addictive beverage. Buy a mate gord, thermos, yerba and ask for agua caliente almost anywhere. No one in MDP leaves home without their mate.
Make the trek to Waikiki beach on the outskirts of town. It's a more relaxed environment than Punta Iglesia or Playa Grande and provides enough room to spread out. They have an excellent surf school there.
Capurro Helado, near Punta Iglesia, is always great on a hot day after cooling off at the beach. Some of the best ice cream in the world.
Take the 221 bus south of the city to hit the nicest beaches, such as Playa Serena.
Go window shopping on Güemes. You'll find the trendiest fashion and some nice cafés to sit and sip coffee while you rest your feet.
Visit the Casino. Even if you don't like gambling, the building is just beautiful - from a different era. The nice promenade along the coast is a great place for exercising or just enjoying a nice view of the sea and the city. You'll find the Casino and very traditional Hotel Pronvincial as you walk on it.
Go see a show! Mar del Plata has a wide range of theatre shows to offer. Get your tickets as soon as you arrive 'cause they run out fast!