To the south of Tucumán, Parque Nacional Campo de los Alisos is a tempting destination, particularly if you have your own transportation. A hilly park at the zone where the montane forest and cloud forest meets the Andes proper, it offers good walking and climbing. There's free camping and a climbers' refugio (shelter). The park entrance is 12km beyond Alpachiri, reachable by bus from Tucumán. The park office in Concepción, 18km before Alpachiri, might be able to help with transportation.
Parque Nacional Campo de los Alisos
Salta & the Andean Northwest