Unfortunately I have to disagree with both Larb and Max – depending on what you mean by ‘largely run by women’ female dominance may be reflected in urban form, albeit likely in very subhtle and nuanced ways. I’m currently writing an archaeology thesis about how gender shaped urban space in 1600s London (which means I can talk/write about this topic until you’re all bored stiff). You will need to be quite imaginative to make it work, though.

First, you say it is a republic, and it is largely run by women. Does that mean that only women can vote? That women are usually more popular electoral candidates? Or do you mean the society is run by women in the sense that households, workplaces, businesses etc are run by women and not men? It makes an important difference which onhe you choose. If the first or second, then Larb and Max are probably right; if the last, then I can make a few suggestions, based on the example from London and my other researches (depending on how far you want to go with this idea, I can recommend various books you might want to read, as well).

Example 1: the simple medieval parish church. A British archaeologist has argued that subtle clues in the architecture of parish churches separate men and women. Mary sits on Christ’s right-hand side, while St John sits on his left. Women would naturally associate more with Mary than St John, so they will sit on the side where he appears. Since churches are often oriented to face west, this means women will generally sit on the northern side of the church. Convents then take this further – an important place in any monastery/convent is the cloister. In monasteries (inhabited by male monks) the cloister is usually on the south side of the main chapel; in convents, it is on the northern side. It is a very subtle difference, but more overt ones might be possible.

Example 2: in London, poor women often had to work to support the household and supplement the husband’s income. However, they were not allowed into the guilds, and so the work they did was usually associated with selling (and buying) goods at market – i.e. men worked in workshops at the back of houses, while women worked in the street and public places. If, in your city, women are equally entitled to participate in various kinds of employment (eg blacksmithing) I can imagine you would have some subtle differences in the city layout.

Perhaps these examples aren’t what you are looking for, though. Fact is, if you are simply switching male/female roles, so that men work in the markets while women work for guilds and that kind of thing, you’ll have virtually no difference; Larb and Max’ll be right. If you have something more specific/nuanced in mind, you can make this city really intriguing and detailed.