Star Trek: 10 Things You Didn't Know About Zephram Cochrane
6. Where You From?
There's some wiggle room here because in the original series episode Metamorphosis Zephram Cochrane is referred to as being "...of Alpha Centauri". Many of the literary works that were produced between that episode in 1967 and First Contact in 1996 continued this and included notes to his Alpha Centauri background.
However, First Contact establishes that Cochrane has never left Earth and indeed hates flying. The flight of the Phoenix is the first time he leaves the planet's atmosphere according to that movie. However with a clever bit of retconning it's revised that Cochrane went to Alpha Centauri some time after the first warp flight.
Subsequent novels have Cochrane as the first man to land on an alien planet's surface (Alpha Centauri B) following a trip there on the Bonaventure (again this is conjecture from Shatner's Federation novel).
The one thing that Trek fans can be certain of is that at some point Zephram did go to that system and spent some time there. Just because it's not been seen yet doesn't mean it's not canon. Interestingly Corbett's Cochrane from Metamorphosis does recognise Spock as a Vulcan which at least does tally tenuously with the end of First Contact.