Our itinerary:
We flew into Buenos Aires. After a few days in the city we planned to take an overnight bus to Tilcara (which is up north, in the Andes foothills). But one of us came down with stomach troubles, too much of that Argentinean beef perhaps, so instead we flew to Salta then took a short bus ride to Tilcara.
After a few days in Tilcara we took a bus back to Salta where we stayed a few days. From Salta we took a bus over the Andes to San Pedro de Atacama in Chile.
After a stay in Atacama we took a bus to the airport in Calama, then a flight to Santiago.
After a few days in Santiago we took the bus to Valparaiso. Finally, we returned to Santiago and then flew home.
Travel tip: We found some Chilean businesses, like the airline that flew us to Santiago, don't accept non-Chilean credit cards. At least they didn't accept them online when we tried to book plane tickets. But we found they would take PayPal, so that served as a fallback.