A fascinating question: I dont have a good answer to this, other than look around the world to see how it’s been done elsewhere.
Here are a few examples:
Stonehenge area. A mix of individual features & collections of features mapped as archaelogical_site. In practice the whole area is one archaeological site and would benefit from a a cleaner hierarchy of tagging of the relevant finds. http://www.openstreetmap.org/#map=16/51.1788/-1.8233
Interestingly, in Machu Picchu, there is both an archaeological_site area, and an archaeological_site node.
The specific locations within the site are tagged with tourism=attraction.
The tourism=attraction tagging could be inappropriate for a complex archaeological site which is not a significant touristic attraction.