We'll just hang around the bridge, not (in) the actual residence.
Why or why not?
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If you want the negated phrase to have the meaning of in, then yes, you do need the preposition in the sentence.
If you do not place the preposition there, people will understand that the preposition around was elided and that that one is the preposition you imply in the second part of your sentence. So, this phrase:
We'll just hang around the bridge, not the actual residence.
Will be understood like to have the same meaning as this phrase:
We'll just hang around the bridge, not around the actual residence.
So, if the meaning you are trying to convey is that they will hang in the residence and not around it, you need the preposition to be expressed:
We'll just hang around the bridge, not in the actual residence.