I do not know of any ways men and women are spatially separated, except for restrooms. Restrooms do sometimes vary by gender. There are biological differences in the fixtures in the restrooms, and sometimes the decor differs. Women's rooms might be pink, for example, which demonstrates a gender bias or sexism. Even the sheer number of restrooms can be significant, as noted in the dailyutahchronicle.com article below.
What spatial separation are we talking about here? Differences in what jobs men and women have? I wouldn't really see this as spatial. Our social structure generally works in such a way that men are privileged compared to women. Our most common roles with regard to family life are an example of this. This is reflected in the fact that women tend to have less prestigious and less lucrative jobs.
Please clarify your qustion if you feel that would be helpful.