Well, if you see "The Andes" as a "tectonic orogeny" then I guess they start at the subduction zone under the Pacific and the "coastal zone" is part of them! However in practical terms "altitude" must have some part to play surely, at least as an initial filter, then taking geographic/geological connections into account? We need of course to accept that the "Andes" are "lower" at their northern/southern extremities.
The main Andean "spine" is fairly clear but the northern division into different Andean ranges and the eastern slopes need looking at more carefully. As this is meant to be a geographical and geological connection rather than a cultural one I wouldn't have thought that sites on the coastal plain such as Chile's Saltpeter works or historic sites such as Chan Chan and Nazca could be defined as being "In the Andes" - the cultures they were part of were "Andean" but that isn't the same surely?
Herewith my initial assignments, some relevant data and quotes via Google where there might be some issues
ALL "IN"? (I have only shown altitude" where it "might" be an issue)
Arg - Los Glaciares (up to 3375 mtrs)
Arg - Quebrada de Humahuaca (2500-3500mtrs) - close enough to the cordillera I would have thought?
Bol - Sucre (2750 mtrs)
Bol - Potosi
Bol - Tiwanako
Bol - Samaipata (1690mtrs) - difficult - Is said to be "In the foothills of the Andes" and at that altitude this doesn't seem "unreasonable"!
Chi - Sewell Mining Town (2000mtrs)
Per - Cuzco
Per - Macchu Pichu
Per - Aprequipa (2380mtrs)
Per - Rio Abiseo (500- 4200mtrs)
Per - Huascaran
Per - Chavin (3185mtrs)
Ecu - Quito
Ecu - Sangay
Ecu - Cuenca (2500 mtrs)
Col - San Agustin (1695 mtrs) Situated in "the Macizo Colombiano, a mountain system where the Andes ranges are divided in the Central and Western Mountain Ranges" so again it stays in??
Col - Tierradentro (2295 mtrs)
All others - Out including
Arg - Ishigualastco (1258 mtrs). "Close by is Mt Famatima. The highest peak in South America outside the Andes" and "forms the western borders of the Sierras Pampeanas of central Arg"
Arg- Cueva de los Manos. It is situated very much part in the "Patagonian desert" and not the "Andes" - which rise very visibly from the plain at this latitude
By the way, on a similar basis, I wouldn't count Manas Park in India as being "Himalayan" - it is only at 60-200 mtres. I know it is described in several places as being "in the foothills of the Himalayas" but in reality it is very much in the plain of the Brahmaputra with totally flat lands to the south and still a few miles to the north before the "Himalayas" start. Rather akin to Chitwan in the Terai I would say -which is slightly higher atbetween 150-815 metres but hasn't been counted . And, good God, it is LOWER than the highest point in the Netherlands which is 322 meters!!!