This diagram from page 100 of The horse, the wheel, and language (2007) by David W. Anthony gives a detailed solution to the exact chronology of Proto-Indo-European (PIE) and its later daughter languages. I quite like this timeline which places Proto-Indo-European within a range of 4500 BCE and 2500 BCE. The author suggests that Anatolian split away from PIE specifically around 4200 BCE.
For kicks, I might be tempted to overlap it with my own chronology of Pre-IE to create a detailed overview of Indo-European diachrony. I'm perfectly fine with cutting off a couple of centuries from my "Late IE" period like this.
Of course, as we all learn more details concerning this fascinating subject, our picture will be prone to modifications but for what it's worth this represents my understanding of PIE's timeline at present.