1492: Conquest of Paradise
Gives a good sense of how Columbus's journey happened, who the key players were, and what the effects of discovery were for both the Native Americans and the discoverers themselves. Unfortunately, it also tries to show Columbus being an awesome hero with a noble heart. They replaced all of Columbus' real life misdeeds with some kind of semi-made-up antagonist that the Guardian suggested might accidentally represent Chris's schizophrenic insanity.
There's lots of errors in small details like costumes, decorations, and time errors, but the movie will still give a good overall picture of Europe's first lasting foray into The New World.
The New World
The story of Pocahontas retold by the director who made The Thin Red Line and Tree of Life. Terrence Malick deals in the abstract, making his stuff seems like poetry. That means its not really a great place to find historical accuracy. (Though, I was told at my last journey down to Jamestown in modern day Virginia that the Fort used in movie was built just across the river from the ruins of the fort you can see today, and that it is painstakingly accurate )
This is mostly a retelling of the early American mythos, even giving us a scene that looks a whole lot like the Thanksgiving that should have happened up in Massachusetts.
The New World will give you a good understanding of the difficulties faced by early settlers both in dealing with a climate much harsher than their own and in dealing with an often hostile native population. I'd say this is a great film for understanding the culture of the time, despite some pretty hard to believe costume choices.
Based on Arthur Miller's play from the 50s. Daniel Day Lewis helps bring this story to life with his Daniel Day Lewisness. Apparently he was so in character that he built his home in the movie with his own two hands. That guy loves historical RP.
The Salem Witch Trials are an infamous story from American history in which women were accused of Witchcraft in a small town and sentenced to death (a commentary on the 1950's McCarthyism). And some men, too. Like The New World, this will give you a good idea of what life might have been like for people living through these times, and the excellent costumes and sets should help bring the whole thing to life.
Unfortunately, due to the scope of the story, you won't get much of a sense about what was actually happening at the time in the greater world.
The Last of the Mohicans
Based on a novel by almost the same name written in 1826, this tells the story of the last remaining members of the tribe called the Mohicans or Mohawk that inhabited the upper mid-Atlantic and parts of New England.
This film will give you some idea of the cultures of both natives and colonists of the time, and is also good for seeing some of the politics that would lead up to the Revolutionary War. Pay close attention to the colonists complaints in this film, as you'll hear shadows of them in the Rev movies. Decent costumes, great sets, beautiful shots (the last bit is filmed in one of North Carolina's great parks, take a trip!)
Like The Crucible, this is a fictional story, so you won't find much here for accuracy outside of battle tacts and world representation.