Is dropping off a friend at a restaurant near his house instead of specifically at his house considered a breach of the oath you made, "By God, at the house," and is expiation required?

If the oath was uttered by you unintentionally, it is considered a laghw yamin (vain oath) and requires no expiation. However, if you intended to make a solemn oath but did not fulfill it (by not going down to the house), then you have broken your oath, and an expiation for the oath is incumbent upon you.