They don't have eyes. The magic that animates them also gives them darkvision, but can they also see normally and react to things further away than 60 feet?
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If the skeleton was blind beyond its darkvision range, it would be annotated as such - see the oozes in Monster Manual for examples of monsters with this sight modifier. Since the skeleton lacks such note, it can see beyond the range of its 60 foot darkvision.