The correct preposition for the action verb “sent” in that sentence is “to,” so the sentence should read as follows:
“The cheque will be sent
to 123 Collin Street, Brisbane, NSW, Australia.”
The big question is, of course, why “to” and not “at”?
We need to use the preposition “to” because “sent” is a verb of motion. Verbs of motion need prepositions of motion to connect them to their object destination. The four other prepositions of motion are, of course, “toward,” “in,” “into,” and “onto.”
On the other hand, “at” is a preposition for indicating place and location. In particular, “at” is used for indicating a point, as in “You’ll find us
at 123 Collin Street, Brisbane, NSW, Australia.” The other two prepositions for indicating location are, of course, “in” and “on.” We use “in” to indicate spaces, as in “We always meet
in an exclusive club,” and “on” for surfaces, as in “There’s a colorful drawing
on the wall,” and for specific addresses, as in “The hotel is
on 123 Collin Street, Brisbane, NSW, Australia.” When a preposition to indicate place and location is used, the verb is usually a form of “be” or a non-motion verb.
For a more extensive discussion of preposition usage, click this link to
Lesson #8 – Specific Rules for Preposition Usage in the Forum’s “Getting to Know English” section.