Not necessarily all of a society, but there have been cases where groups (typically religious ones, but not always) ventured out into the more western parts of the United States to form a more "utopian" version of government and economy, notably during the 1800s.
One such group, called the Harmonists, moved to Indiana. They followed a man named George Rapp (a farmer of German descent), and were sometimes referred to as Rappites. Besides their move to celibacy at one point, they were extraordinarily religious and he gained a rapport (no pun intended) through the exclamation of various "visions" in which God (he claimed) told him how to build great buildings.
Anyways, Rapp developed a pretty good community in Pennsylvania, but eventually decided (in 1815) to move to Indiana, founding a village they called "Harmonie".
Some bits about how they made life more sustainable (and also religiously conservative by today's standards): rough, homespun fabric for clothing, constant work building and farming, and a very self-sufficient (at least, for the village) way of life.
They did actually grow rich, reportedly, from this venture, before the village was sold to a Mr. Robert Owen in 1824. He, too, planned to make a more "utopian" society, but went about it in different ways. He changed the village's name to New Harmony, and mentioned that inequality would have to happen now, because he wanted to spend some money to convince people who were of "big intellectual caliber" to settle there. This did happen, by the way, to a degree. However, the constitution was revised 7 times, there was a lot of tension in the community, and eventually it simply formed the nucleus for new communities that surrounded it.
This is just one instance, however. They didn't necessarily abandon technological advancement to great degree, or anything like that, but they abandoned ways of life that included amassing wealth, abstained largely from luxury, and worked in a very self-sufficient, bubble-esque type of way. There were myriad others who tried, and many failed.
Doctor Keil, a figure who established a community in 1845, originally started his community in Bethel, Missouri, before moving it to Oregon.
There were accusations, particularly by one former member, that Keil was the sole benefactor and "owned" all of the property (amounting to $120,000 total in 1870, between 324 people). These were later proven unfounded, when it was found that Keil was merely a trustee for the property, and it was divided equitably when he died in 1877.
What was the society like, then? Well, at first they were a farming group, and they gained some measure of wealth in this way, before moving to Oregon in 1855. Missouri, a prairie area, was naturally going to be arable, and so it was when they went to work on it.
When they moved, one account put them at having less than 50 men (no general population number mentioned, unless he's including women, which I doubt), but it was somewhere close to 50 men at least. They reached Portland, but Keil set out again in 1856 to the Willamette Valley, where they finally founded Aurora (not to be confused with the city in Colorado of the theater shooting).
The colony, being around 25 in number, lived in one log cabin (that was built in 1849) for some time together. They had a small sawmill, a gristmill, and they built another mill. They also manufactured lumber.
They would work at cutting down trees, unless there was no meat (in which case they went hunting), and every group of 4 workers had to cut down a tree before breakfast. It was very industrious and hard-working life, but it went very well. Jacob Miller, one of the community members, asserted that Keil's social philosophy was communistic, but based (as he saw it) entirely on the Bible and the disciples, especially the idea that "they had all things common, neither were there any among them that lacked."
Everyone was allowed to take anything they needed from the general store, and anything left would be sold before placing the money in the common treasury (belonging to everyone) so it could be used to buy things that weren't manufactured in the community. Individual property wasn't practiced, and the society was very open about sharing anything that they did not need themselves. Again, this is not necessarily a case of giving up technology per se, but a case of changing their ways of life; they were, in many ways, communists who managed to make it work in their own little bubble. Not in all ways, to be sure, but in many ways indeed.
Both of these communities, and many others that I haven't even gotten into (gotta get back to writing my paper!) were fascinating examples of attempts at utopian societies in history, and these are just two of the examples in the United States in the 1800s. I highly recommend reading the sources I mention below, as they're both interesting. The first attempts to take a sociological look at the Harmonist Movement, and the second is an account drawn together by speaking to members of the Aurora community of what life there was like.
Hope that helps!
The Harmonist Movement in Indiana Elizabeth Smith Denehie Indiana Magazine of History , Vol. 19, No. 2 (JUNE, 1923) , pp. 188-200
The Aurora Community Emanuel Keil and H. S. Lyman The Quarterly of the Oregon Historical Society , Vol. 2, No. 1 (Mar., 1901) , pp. 78-93