The answer lies in the order of "would do you".
If the order were "would you do", then when why and where are possible. "Whose" is not possible at all.
"Who would do you such a thing in this day and age." This means somebody was kind to you. They did you a favour. You'd only get that either by chance or knowing the "do someone a favour" pattern.
"A favour" becomes "such a thing". Favours are common, but maybe this favour was special. A favour like that = such a thing.
Who would do you a favour like that in this day and age?
Who would do you such a thing in this day and age?