The ancient Inca city of Macchu Picchu, perched on a ridge in the Andes Mountains of Peru, had been built at a high enough altitude that it often makes modern-day tourists from lower elevations sick with oxygen deprivation.

had been built at a high enough altitude that it often makes modern-day tourists from lower elevations sick with oxygen deprivation
had been built at so high of an altitude that it often makes modern-day tourists from lower elevations sick from oxygen deprivation
was built at a high enough altitude that modern day tourists from lower elevations often become sick with oxygen deprivation when visiting the city
was built at such a high altitude that modern-day tourists from lower elevations often become sick from oxygen deprivation when visiting the city
was built at so high of an altitude that it often makes modern-day tourists from lower elevations sick from oxygen deprivation

The correct choice is D. Can someone provide clear rules for using the following idioms:
1) enough X that Y
2) such a(n) X
3) so X that Y

I understand the other issues with this sentence (tense, etc.)

The sentence correction strategy guide, if you have it, provides an admirably detailed guide to this distinction (and others you didn't mention here, like 'so as to...')

Possibilities #(2) and (3) are generally used by writers who want to emphasize the EXTREME DEGREE of whatever they're talking about. (2) is used when X is a noun, and (3) is used when X is an adjective or adverb.

Possibility (1) conveys a meaning of sufficiency or adequacy, often combined with a sense of purpose in achieving that adequacy. With this in mind, the third choice below (high enough altitude...) means that the Incas actually had the purpose of depriving future tourists of oxygen in mind when they constructed the city!

Sample:
Was you score high enough to get in? = was it sufficient? did it achieve the purpose? (no reference to extreme quality - just adequacy)
Was your score so high that you got in?
Did you get such a high score that you got in? both --> the admissions standards under discussion are unbelievably selective; the speaker is emphasizing the idea that the listener would need incredibly high scores to 'get in'