jf02, sure I’d characterize male drivers as gallivanting when applicable. I didn’t characterize all female driving like that, I specifically referred to the times it’s applicable. Though the issue mentioned from the Shulchan Aruch is applicable to females and makes their public gallivanting more problematic than that of males.
As far as important, in the context of the aforementioned Shulchan Aruch, it would mean any unavoidable travel.
etzhar, See above regarding important. Limud Torah is important. And if it requires the wife to go outside in public as a result, it almost surely would qualify for the limited times the Halacha (above mentioned S”A) permits a wife to go out.