Pre-Columbian population figures are a matter of considerable debate. New information is constantly being uncovered, and old colonial era documents once thought to be hyperbole are more often then not validated in the process. The numbers are always shifting (generally upwards), so pinning down specifics like the precise population densities is somewhat difficult. Pre-Columbian demographics are a moving target.

With that in mind, there are some generalities we can make. I can only speak about the eastern portion of the continent; I know there were relatively dense populations in the Pacific Northwest as well, but that's significantly outside my area and I'll leave it for someone else to hopefully address.

Cahokia famously sets the high water mark for population centers in the east. Located near modern-day St. Louis, Cahokia was once home to several thousand people at its peak in the early 13th Century. But whether "several thousand" means something as low as 5,000 or as high as 40,000 is debated; 20,000 seems to be an estimate most archaeologists can tolerate for the site. If the high end estimates are right, though, it would have been one of the largest cities in the world at the time. It also wasn't alone in the area. Cahokia likely served as the capital for a large polity, incorporating several notable communities nearby, as well as extending its influence far and wide over the eastern part of the continent, especially into the Southeast.

Long after Cahokia went into decline, polities influenced by it dominated the American Southeast. Of those, Apalachee is one of the best known because it was encountered early and often in the century after Columbus. Apalachee was located between the Ochlockonee River and the Aucilla River (the Aucilla is not labeled on that map, but it is the river that separates separates Jefferson County from Madison and Taylor Counties). It had too major towns, Anhayca and Ivitachuco, on its western and eastern borders respectively, and several smaller towns. In 1608, a Spanish priest named Martin Prieto visited Ivitachuco, where he was greeted by (according to his estimate) some 36,000 people, which he thought was the entire Apalachee population. This is one of those early reports that was once thought to be exaggerated but has since been validated. If anything, Prieto's estimate is under-reporting the population of Apalachee. He has come to help negotiate a peace between the Apalachee and the Timucua (themselves a very populace, but political fractured, people living in northern Florida east of the Suwanee River and in neighboring portions of southeast Georgia, with an estimated population of perhaps 200,000). Because of the priests diplomatic endeavors, a council of 70 prominent Apalachee political leaders had been summoned to Ivitachuco. This certainly would have drawn a crowd, but it was unlikely to have pulled the entire population of the region into the capital (Anhayca had been the dominant one of the pair, but over the 1500s, power shifted to Ivitachuco). This has caused the estimate to shift even higher, perhaps as much as 60,000, for the entire Apalachee territory, a relatively compact area no more than 40 miles across in any one direction.

With the Apalachee and the Timucua, among other groups, Florida was certainly a contender for most densely populated region in what has become the continental USA and Canada at the time of Contact, but I should warn you that there is significant selection bias here. Florida was close enough Spanish controlled areas in the Caribbean and Mexico to receive frequent early visitors, so we have a lot of documentary evidence along with archaeological evidence of life there before the epidemics began (which were one of the causes responsible for the particularly severe population decline in Florida - the slave trade being the other notable one). Beyond Florida, information gets sketchier.