I can think of quite a few good books you may like. My first suggestions would be James Patterson's Grand Expectations and Restless Giant. The former is a history of the U.S. from the end of WWII to right before Watergate; the latter is a history from Watergate to Bush v. Gore. Both books are a part of the Oxford History of the United States series, which is the go to source for anyone wanting academically thorough and very readable narratives. Literally every U.S. history professor I've come across just uses these books to structure their intro lecture courses.

Overviews of the 1960s and 1970s:

Terry Anderson The Movement and the Sixties

Jeremi Suri, Power and Protest

Edward Berkowitz, Something Happened

Bruce Schulman, The Seventies

Thomas Borstelmann, The 1970s

Overviews of the the 1970s and later:

Godfrey Hodgson, More Equal than Others

Sean Wilentz, The Age of Reagan. Gives a very readable overview of the period from 1976 to the early 2000s. Good critical account of Reagan and his legacy.

Daniel Rodgers Age of Fracture. This book is very highly regarded (won the Pulitzer not long ago) but is also pretty dense. It may be better to read through 1 or 2 of these other overviews before reading this.

If you're wanting to look at U.S. postwar history within an international context, by far the best overview is Global Interdependence: The World After 1945, edited by Akira Iriye.

Overviews specifically on the 1980s:

Gil Troy, Morning in America: How Ronald Reagan Invented the 1980s

Robert Collins, Transforming America. Gives a very positive outlook of the Reagan administration.

John Erhman, The Eighties

The end of the Cold War was obviously a major event in U.S. history. To look at U.S. history during that time within an international context, you can check out The Fall of the Berlin Wall: The Revolutionary Legacy of 1989, edited by Jeffrey Engel or The Global 1989: Continuity and Change in World Politics, edited by George Lawson, et al. (this one would actually also be a good book on the 1990s, too).

As for the 1990s, there hasn't been too many overviews written yet. A good one, though, is Haynes Johnson's The Best of Times. If you're into political history, Steven Gillon's The Pact is a great book about the relationship between Bill Clinton and Newt Gingrich. Lastly, you may like David Halberstam's War in a Time of Peace, which focuses on U.S. foreign policy but also gives decent coverage of U.S. domestic politics at the time.

Most other history books I've come across concerning the 1990s as a whole deal specifically with U.S. foreign policy.

If you can perhaps narrow down your interests even more, I can recommend some more books (ones that aren't simply overviews). There's just too many to list on such a wide variety of topics; even to say you like cultural history is a bit broad. What do you consider cultural history? If you like Perlstein you may like some books on the rise of conservatism in the U.S.

Age of Fracture by Daniel T. Rodgers does an excellent job of explaining the sociocultural effects of postwar America.