In Union County, New Mexico, lies Sierra Grande, a significant shield volcano. Various sources proclaim Sierra Grande to be North America's largest "free-standing" mountain. Some call it the largest free-standing mountain in the United States. However, a pretty good case can be made that Mauna Loa and/or Mauna Kea are larger. That is probably why several sources claim Sierra Grande is North America's largest free-standing mountain. By limiting the scope to North America, the Hawaiian Islands are excluded.
Some questions of definition arise regarding this subject. What, exactly, is a free-standing mountain? Let's rule out the big volcanos of the Cascades since they are part of a well-defined major mountain range. Similarly, we may omit the volcanos on the Aleutian Islands. Certainly, some of them could be considered to be free-standing on their own islands, but at the same time they belong to a named mountain range, the Aleutian Range.
What is meant by largest? Let's consider the base of a mountain to be the lowest closed contour which encircles it and remains near the summit. Then look at the volume that would be occupied by a pyramid with a base area equal to the area within that contour. The height is the height above the base contour. Note that there is still an element of subjectivity here, because different people will have different ideas of what distance is "near" the summit. I try to pick something that seems reasonable and go from there.
Is the massif a single mountain or a mountain range? This issue either allows a peak to be considered or rules it out, because if we consider it to be merely another peak in a whole range of them, then it does not qualify as free-standing or stand-alone.
Since the answers to the questions above are somewhat arbitrary and subjective, the designation of any peak as the largest will be debatable. Nonetheless, I will propose some that arguably top Sierra Grande.
Take the Black Hills for example. The name causes us to consider that geographical feature as a range of hills. Despite the name, however, geologically, the Black Hills consitute a dome mountain. Note how in Sydenham, S. & Thomas, R. Mountains [Online] www.kidcyber.com.au  the Black Hills are given as an example of a dome mountain (singular). Tracing the 5000-foot contour around the Black Hills surrounds an area of about 1870 square miles. Harney Peak rises 2242 feet from that base. A pyramid with those dimensions would have a volume of 265 cubic miles, far more than the 5 cubic mile guesstimate that a similar process yields for Sierra Grande. See the table below.
But if the Black Hills are taken to be a mountain range, we need to look elsewhere. How about Steens Mountain in Oregon? Now we have a feature which is in name a single mountain. It extends over an area of 450 square miles rising above the 5750-foot contour and rises nearly 4000 feet from that base. A 4000-foot pyramid with that big a base would contain a volume of more than 100 cubic miles. However, despite the singular name, one might still argue that Steens Mountain is actually a mountain range.
Look down the list to Navajo Mountain. By all accounts this is a single mountain that stands alone in southern Utah at the border with Arizona. It occupies a somewhat smaller footprint than Sierra Grande, but is twice the height above base. So, a plausible argument can be made that it is a larger stand alone mountain.
In conclusion, I won't flatly claim any particular peak to be the largest stand-alone mountain in the US or in North America. There are just too many subjective factors involved in choosing one. Regarding Sierra Grande, an accurate statement without hyperbole, is one describing this shield volcano as the largest in northeastern New Mexico. See http://www.waymarking.com/waymarks/WM5DG6 and consider visiting Sierra Grande to see it in person. While you're in the area visit Capulin Volcano National Monument, too.