I believe this is "Race Against Time" by Piers Anthony. Below are some descriptions from various sites and a shot of the cover.
The plot description matches perfectly with what you have described.
"John Smith is just a typical teenager growing up in a typical American town...Or is he?
He has a dog -- that can climb trees and understand very complex commands. He has parents -- who watch him constantly, taking notes when they think he's not looking. He has a girlfriend -- a girl he's never met, whom he has been told he must marry.
John knows that something is wrong, but until he crosses the boundary fence late one night, he doesn't realize just how much. For wherever he lives, it's definitely not America!"
From Kirkus Review:
From an innocuous beginning -- a boy and his dog walking through the fields -- layer upon subtle layer is overlapped to develop a superior science fiction vision. The boy, John Smith, only extant caucasian male and raised in an enclave environmentally geared to America, 1960, is destined to be mated with caucasian Betsy, similarly raised, in a world populated by a totally integrated race appropriately called "Standards." Through a series of errors (or are they?) they and the society's two other "purebred" pairs (one African and one Chinese) escape their enclaves and investigate the Standard world around them -- a world so completely envisioned by Mr. Anthony that he occasionally loses the reader in a reference to some aspect hitherto unrevealed. (This however is not a serious flaw; in fact, it contributes to the compelling style of layered revelation.)
The six eventually learn
that they are products of procreative banks preserved through the centuries and that Standard is Earth after pollution and human-instigated plague wiped out most of the population. There is considerable ambiguity about the Standards and their true purposes, and the author's apparent assumptions about racial/ethnic interaction may be debated, but it is provocative in the presentation and even the stereotyped characters are believable considerating the nature of their nurture.