Good choice. The best choice, even though it's 180-odd years old.
Distant competitors might be Crevecoeur's Letters from an American Farmer and Benjamin Franklin's Autobiography.
At some point in history it got hard to write about "America" as a whole.
Maybe Henry James or Mark Twain or Hemingway or Fitzgerald had something to say in fiction about the American character.
For the closest thing to a modern Tocqueville maybe we have to go back to David Reisman's The Lonely Crowd.
The Lonely Crowd, now there is a blast from our school days. I noticed LS paraphrasing C. Wright Miles in a post the other days. Some of that rhetoric is just part of the english language now
I wish I had read some of Richard M. Weaver back in those days in the 60s instead of waiting until the 80s. More Weaver and Kirk would have helped the thinking that came out of that era.