Although the United States, which is a vast and varied country with many interesting features of topology, has many communities that could be considered remote, picking the most remote one is difficult. And, in fact, I will not try to provide a definitive answer, but will instead discuss a number of different places and how they fit in with several criteria.
For one thing, there are a number of different ways to find an isolated place. Simple distance from other settlements does not suffice, since that doesn't take into account the influence of difficult topography or the possibility of reaching the town through other ways. The lack of services inside a community will also be taken into account, since in many places, the further a town is from other towns, the more likely it will be to have services that a small town would normally not have. In fact, lets look at our first example, which may be the first that would spring to someone's mind:
Barrow, Alaska, is the United States' northernmost city, lying 320 miles above the Arctic Circle. There are no roads that connect Barrow with the rest of Alaska. To the south of it lies several hundreds of miles of tundra before you can reach anything larger. So is Barrow, Alaska an obvious choice for most remote town in the United States? Perhaps, but there are a few more facts to be remembered. First, like many other cities and towns in Alaska, Barrow has an airport with regular service. It is also large enough that, as mentioned, it has many services that such a small community would not normally have. It has a community college and a hospital. In other words, while quite geographically remote, it is tied into the wider world quite a bit.
Although I am sure that there are many other towns in Alaska, either around the North Slope or perhaps in the Aleutian Islands, that could easily be elected as America's most remote location. Although even small Alaskan communities usually have general aviation airports, there are probably some that do not. The village of Atka, Alaska, population 95, and some hundreds of miles away from anywhere else populated in the Aleutians, has its own airport. Yet there probably is a town somewhere in Alaska that would obviously capture the most isolated title.
However, we might want to narrow our question down to just looking for the most remote town in the coterminous United States. This town will be somewhere West of the Mississippi, and probably located somewhere in the Great Basin or Rocky Mountains. In fact, when looking for uninhabited places in these regions, we have somewhat of an embarrassment of riches.
Not quite at random, but out of many possibilities, I have taken a look at Austin, Nevada, elevation 6605 feet, population 340. Austin lies on US Route 50, The Loneliest Road in America, and is close to 200 miles, in each direction, from any towns that are larger. However, Austin has two strikes against it as far as remoteness goes: it lies along the interchange of a federal highway and a state route, and it also has its own airport located just outside of town. Also, and this perhaps marks me down as a Rocky Mountain chauvinist, the great basin's topology, while quite dramatic, is usually not quite as dramatic as the ranges of the Rocky Mountains.
West Yellowstone, Montana could be considered a very remote place, especially if we had weather to our criteria. It frosts and snows in West Yellowstone throughout the year. However, since it is one of the main entrances to Yellowstone National Park, West Yellowstone probably has more people passing through it then some towns 20 times its size. The same is true of other, somewhat more obscure towns, such as Stanley, Idaho. While seemingly small and remote, these towns gather visitors for just such this reason. In some ways, this is akin to the interesting number paradox: the most remote town in the United States often attracts visitors, and attendant services and transportation, simply because it is remote. However, somewhere along the many backroads that go in and out of the many subregions of the Rocky Mountain, there is some town down a county road that is obscure enough to not be a tourist attraction. And which one of these is truly the most obscure remains a question that can never be answered. Would it be Polaris, Montana? Elk City, Idaho? Some town in Colorado or New Mexico that I don't even know exists?
And perhaps I am even narrowing my search too much. There could be other reasons why a community could be isolated. Kalawao County, Hawaii, is a tiny peninsula with barely a hundred residents, almost all of whom are lepers. The isolation of this community is probably qualitatively different than any other.
So the ways that a community can be isolated are manifold, and we have gone from the permafrost and vast distances of northern Alaska to the somewhat cloistered life of lepers on a small, tropical peninsula. None of these can really be said to be the most remote, but all of them are good candidates.