Okay, I'll bite:
0) I'm not sure it's best that anyone exist at all, but for the sake of a post let's assume they should.
1) Assuming the resources (which seem to be implied in the ability to change the gender ratio in the first place) nix men entirely. I'm probably more skeptical than the average LWer that traditionally male pathologies are inherent to my sex, but there's a decent chance I'm wrong about that, so there's that. More importantly this gives public institutions veto power over the creation of new people in a way that isn't bodily intrusive.
2) People own their bodies; the state owns the means of production, which are rented out by cooperatives. Investment decisions are guided by prediction markets. Public goods are provided by the state on a universalistic basis. (This is assuming we still have to deal with scarcity.)
3) Raising children is a compensated service to the state, in principle not separate from other forms of market production. (More tightly regulated, obviously.) Reiterating my caveat that I'm more of a constructionist than the typical LWer, eugenic opportunities present themselves, as do opportunities for speeding up the destruction of ascribed ethnic status.
4) Legislators chosen by sortition, either from the general public or some sort of ascetic public service corps.
5) If we have the resources, Destroy Nature (but keep public gardens large enough to hike in.) If we can't get rid of most other animal life, at least get rid of factory animal farming.
I don't think this would be fully stable (I don't think I could endorse anything that would) and I don't doubt it would horrify plenty of people, but if I could press a button this is what I'd press it for.
Assume for the time being that it will forever remain beyond the scope of science to change Human Nature. AGI is also impossible, as is Nanotech, BioImmortality, and those things.
Douglas Adams mice finished their human experiment, giving to you, personally, the job of redesigning earth, and specially human society, according to your wildest utopian dreams, but you can't change the unchangeables above.
You can play with architecture, engineering, gender ratio, clothing, money, science grants, governments, feeding rituals, family constitution, the constitution itself, education, etc... Just don't forget if you slide something too far away from what our evolved brains were designed to accept, things may slide back, or instability and catastrophe may ensue.
Finally, if you are not the kind of utilitarian that assigns exactly the same amount of importance to your desires, and to that of others, I want you to create this Utopia for yourself, and your values, not everyone.
The point of this exercise is: The vast majority of folk not related to this community that I know, when asked about an ideal world, will not change human nature, or animal suffering, or things like that, they'll think about changing whatever the newspaper editors have been writing about last few weeks. I am wondering if there is symmetry here, and folks from this community here do not spend that much time thinking about those kinds of change which don't rely on transformative technologies. It is just an intuition pump, a gedankenexperiment if you will. Force your brain to face this counterfactual reality, and make the best world you can given those constraints. Maybe, if sufficiently many post here, the results might clarify something about CEV, or the sociology of LessWrongers...