The city centre is walkable, if hot. The main sights — the plaza, the cathedral, the folk museum — are all within easy walking distance of each other. Taxis and remises (private hire cars) are inexpensive and are the sensible option in the heat.
For the national parks, a rental car or an organised tour is the practical choice. Talampaya National Park is about 180 km north of the city on RN 26, and while the road is paved, there is no public transport to the park entrance. Several agencies in the city run day tours to Talampaya and to the combined Talampaya–Ischigualasto circuit. Ischigualasto is in San Juan Province, so the combined tour crosses a provincial border — tours handle the logistics and it adds no complication for visitors.
Car hire is available at the airport. Having your own vehicle gives considerably more flexibility, particularly if you want to stop at smaller sites along the way or spend more than a few hours in the parks.