The sentence should describe how the old man looked, in a manner that fits the context of the action.
"Cautiously before" is the most appropriate as it maintains the correct adverbial form to describe how the action of "looking" was performed.
The other options are incorrect because they either disrupt the meaning or structure of the sentence.
Conclusion:
The correct phrase is "cautiously before" because it conveys the manner in which the old man looked before crossing the street.