I have seen all sorts of posts on the Internet about when he travels to, but most of them are doctored to make people repost them. I originally saw one picture that showed the deLorean dash showing a date in 2012, like this one.
This could be an original shot from the movie before the panel was tampered with
So what is the real date he traveled to?
Snopes had this to say
All of these japes are easy to identify as hoaxes by simply remembering the number 30: The original Back to the Future Part film was set (and released) in 1985, and in that film Marty McFly traveled thirty years back in time, to 1955. In the sequel, Back to the Future Part II, Marty traveled thirty years forward in time, from 1985 to 2015. The latter is therefore the year Marty will "return" — not 2012 or 2013 or 2014, but 2015. The date of 21 October 2015, to be precise: Read more at http://www.snopes.com/inboxer/hoaxes/bttf.asp#wb6jI6D7iAwzE097.99
Precisely at 4:29 PM Wednesday October 21st, 2015
The Second image in the question is another Photoshop spoof and not from the movie and is mentioned in the Snopes article above.
