Most people visit the peninsula with a day tour organised from Puerto Madryn. The tours usually start at 7:30 and return between 6:00 and 7:30 depending on the tour company. Destinations are typically the visitors center, Puerto Pirámides for whale or marine fauna watching depending on the season, Calleta Valdes/penguin area and Punta Norte. An advantage of a tour is the English speaking guide.
For more independence rental cars are available to explore the peninsula. The entrance fee is valid for a single entry and not depending on how many days you stay.
If you are only interested in the whales, just take a bus to Puerto Pirámides and pick a boat-tour from there.