Assuming the interpretation of the film is such that David wakes up in the real future at the end of the movie, is there any clue about the date and nature of this future?
No. Neither the film Vanilla Sky, nor the film on which is was based (Abres los Ojos) deal with the world of the future. Both films end pretty much identically, with the protagonist supposedly waking up some 150 years after he was frozen. As far as we can tell, the future is more advanced, but by no means utopian.
VENTURA: Yes. Just like Benny the Dog. Your face and body can now be fixed, of course. But it's very different out there now. Your finances won't last long. Your panel of observers are waiting for you to choose. There are no guarantees. But remember, even in the future, the sweet is never as sweet without the sour.