Best books on US history:

"The First Salute" - Barbara Tuchman
A look at how the political rivalries within the Royal Navy led to the British loss of the American Revolution

"Miracle at Philadelphia" - Catherine Drinker Bowen
Story of the Constitutional Convention of 1787

"American Scripture" - Pauline Maier
Background on the Declaration of Independence

"The Ideological Origins of the American Revolution" - Bernard Bailyn
The title says it all. Bailyn is probably about the best US Historian around today.

"The Creation of the American Republic, 1776-1787" - Gordon S. Wood

"Novus Ordo Seclorum: The Intellectual Origins of the Constitution" - Forrest McDonald

"Democracy in America" - Alexis de Tocqueville (1835)
de Tocqueville was a French Nobleman who spent several years traveling the US in the early 1830. This work has been highly regarded since its original publication for its unique "outsider's perspective" of life during the early decades of the Republic.