From Salta the most easily accessible inscribed site would be the ruins at Santa Rosa de Tastil. It's 110 kms from Salta Capital and takes about 1.5 hours according to Google Maps. Santa Rosa is extremely rural with neither electricity nor mobile phone signal, so be prepared accordingly if you travel there. The ruins are about 2 kms outside the village.
For the section at Valle Grande it is easier to reach it from Jujuy Capital rather than from Humahuaca. Although merely 80 km from Humahuaca, the road seems to be in a bad condition and Google Maps estimates the drive with 4 (!) hours. From Jujuy Capital there is a national road of decent quality leading to the NP of Calilegua (worth visiting on its own right). From there it's a shorter drive. Mind the fact that Google Maps hasn't updated its depiction of Ruta Provincial 83, which now connects to the south. Cf. http://www.productoyungas.org.ar/turismo3.asp?id=34&nivel2=rutas%20escenicas