Many of the utopias from the golden age of science fiction (long before nanotech) had recognisable humans, who were not immortal and whose robots were good butlers, at best. While for the sake of plot they generally had faster than light travel, that isn't actually a requirement for the human species to spread out to the stars.
If you'll grant sub-light interstellar travel, then all these become possible. Let groups bid on planets, set a pre-requisite that the group survive in a bio-sphere for 3 generations, as a test to see if their proposed society is sufficient stable to avoid shooting each other, then ship them off.
That then transforms the question into what sort of meta-Utopian society would support investing the time and effort required to mine the asteroids, set up massive solar powered anti-matter production factories, and keep seeding the universe generation after generation?
Given said technologies would also offer plenty of ways for individuals or small groups to blow up the Earth, it would need to be either a very tightly controlled one, or a very sane one. Or possibly both. Heavy investment into improving education, parenting (and possibly designer babies). And getting people used to lack of privacy and the goldfish bowl surveillance society.
Can that be done without changing human nature beyond existing parameters? Well, the boundaries of the current parameters are actually pretty wide: they include sealed nuclear subs, monastic communities, military academies with no privacy, and life-logging 24/7 facebook-blogging twitter-addicted web-cam-dorm residents.
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...