Your question: Is the writer trying to imply "garage" is a place to stack stuff in? Is so, why didn't he use "attic" or something else?
Yes, he is saying the garage is a place that we CAN stack stuff in (not everyone does, though), and he could have used another word like attic, but then it would lose the humor, where garage and garbage sound similar, and the garage is one more step in the sequence to changing into garbage, and perhaps, he implies, a natural step in the sequence.
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