In AE you can leave out 'house' or 'place' with a noun or proper name:
• I went around to John's yesterday.
• The kids are over at the neighbors'.
• The block party was at the Friedmans' / the Williamses'.
And you can leave out the word 'house' or 'place' the second time and substitute a pronoun:
• How much time do you want your inlaws to spend at your place or your children to spend at theirs?
• A: Your place or mine?
B: Oh, mine, I guess. No, on second thought, yours. Mine's a mess this week.
But you can't use a pronoun the first time in the sentence without 'house' or 'place':
• Come over to my place and we'll have a cup of tea.
• I really like my grandparents. I often stay at their place.
BTW, there's no such word as *their's with an apostrophe, even though many native speakers add apostrophes where they shouldn't.
(attributive or adjectival -- used before a noun, to describe it)
my, your, his, her, its, our, their
(predicative or nominal -- used alone, to replace a noun)
mine, yours, his, hers, its, ours, theirs
mine's = mine is
it's = it is