Can I use "here" instead of "the path"?
Yes, you could say "here" instead of "the path", however, this would change part of the meaning of the sentence. "Coming up the path" means that she is specifically walking up a pathway to somewhere else. If you replaced this with "coming up here", it would not give details as to where she is walking from, but only implies that she is walking towards the speaker. So both sentences express that she is walking up towards something, but there is a slight difference in the location of where she is walking.
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