In the following sentence, should "Who" or "Whom" be used in the blank space?: To ___ should this be addressed to?
Whom (but you don't need the final "to".....)
It depends on whether you are referring to the object (the noun that is having an action done to them) or the subject (the noun that is doing something).
If you're having something addressed to you, you're the object. If you are writing the address, you are the subject.
"Who" is the subjective form, and "Whom" is the objective.
But as the sentense starts with "To..." you don't need another "to" at the end. You just say "To whom should this be addressed".