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I plan to stop by her place next week.
Literal
Next-week her [possessive-の] place [to-に] drop-by [intention-つもり] is.
立ち寄る is a compound verb: 立つ ('stand') + 寄る ('approach / draw near') = 'to drop by / stop by / make a brief visit.' Common in travel and social-visit contexts. の+ところ is a way to refer to someone's place or whereabouts without being specific about the exact location.