Ideally, I'm looking for a book that covers American history after the Revolution and before the Civil War. Ideally one book, single-volume -- but all recommendations are appreciated!
While it depends on exactly what you're looking for, here are a few recommendations broken down by topic and time period. If you're looking for one book in one volume, try Howe's What Hath God Wrought. It starts after the War of 1812, but it's hard to find one that starts earlier without it being a textbook!
Immediately following the Revolution:
Woody Holton Unruly Americans [Address the impact of democracy on the coming the Constitution]
Saul Cornell The Other Founders [Looks at the Anti-Federalists during the Constitutional debates]
Maya Jasanoff Liberty's Exiles [A look at the Loyalists and the "Spirit of 1783" that transformed the British world.
John Phillips Resch Suffering Soldiers: Revolutionary War Veterans, Moral Sentiment, and Political Culture in the Early Republic [How the United States government largely failed the veterans of the Revolution]
Politics of the early 19th Century:
Joyce Appleby Inheriting the Revolution [How the men born during and after the Revolution shaped early 19th Century US]
Alan Taylor The Civil War of 1812 [Exactly like what it sounds like. Taylor is an amazing writer]
Daniel Howe What Hath God Wrought [Winner of numerous prizes. Covers American politics from the War of 1812 through the 1850s]
Alfred Young The Shoemaker and the Tea Party [An interesting study of the changing meaning of the American Revolution during the 1820s and 30s]
Early American Economy
Charles Sellers The Market Revolution [Rise of industry in the United States]
Bruce Laurie Artisans into Workers [Social Impact of early industrialization]
Slavery
Edward Baptist The Half Has Never Been Told ["The alliance of the lash and loom" told through the domestic slave trade.]
Walter Johnson River of Dark Dreams [Slavery in the Mississippi Valley Region]
Other Patricia Cline Cohen The Murder of Helen Jewett [Murder, sex, prostitution and the story of the early American middle class]
That might be a bit much; however, I couldn't resist. I'm open to give more insights if you'd like. Enjoy!
I think that the best source for synthetic narrative history of American history is the Oxford History of the United States. Daniel Walker Howe's What Hath God Wrought, which covers 1815-1848, is perhaps my most frequently recommended book (that shouldn't be surprising - this is the time period of my own speciality). I know that doesn't get all of your requested time period, but it gets to the heart of antebellum America. The Gordon Wood volume Empire of Liberty and McPherson's Battle Cry of Freedom are both excellent.
That gives you three volumes, but it's hard to get a single volume to cover that much time while also covering political, economic, social, cultural, military, and other branches of history.