I agree with the rest that it was really happening, however, with a bit different reasoning. The whole ending is done in a way that it gradually reveals that Bruce had made it:
We see Gotham finally accepting the Batman as a hero, also confirming the overall belief that he's dead.
We find out that Blake is named Robin, which - at the moment - seems like just a minor, unimportant detail.
Then we find out that the autopilot was fixed six months ago, which is supposed to spark a hope that Bruce just might have made it.
Back to the Missing items, Bruce's mother's pearl necklace is gone. Another spark of hope. I realize that someone else might have taken it, but it wouldn't be in the spirit of the ending. But still, at that moment, it's just rising our hopes... maybe Bruce is really alive...
We see Blake coming to a strangely familiar waterfall, and we start realizing who sent him the package. It could have been Alfred, of course, but I think he saw the Batman as a curse, so it's not like he'd like to see it passed on.
We see Alfred entering that cafe in Florence, the exact same scene as from his story before, and we start realizing that we'll soon see Bruce, happy and Gothamfree.
Blake scenes start mixing with the others, building up to the joint climax. Blake's part, as we are now sure is going to happen, is his gaining the access to the Batcave.
We see Gordon at the rooftop, where we know the Batsignal used to be. We see something catching his eye. We don't yet see what it is, but it's an easy guess, and yet another confirmation that Bruce is leaving subtle signals to his surviving friends, without making a direct contact.
The final climax:
- Blake in the cave, among the bats, as once was Bruce. We now know where Blake is, and are pretty sure who sent him there.
- Gordon approaches what caught his eye, and we now see that this really is a Batsignal. We also see Gordon's face, which confirms our realization that Bruce is alive, and we're just seconds away from seeing him again.
- Back to Blake, and the same face of realization (that Bruce is alive), ending with his approach towards the platform.
- Back to Alfred, with yet again the same face of realization, as he has obviously seen someone he knew. He nods, and we finally see Bruce alive. Alfred leaves, as in his dream, without talking to Bruce, but they both know that Bruce had made it. That he's happy. And now the audience knows it as well.
- The final scene is of Blake rising on the platform, confirming that the Batman's story is over. If there is more, it can only be Robin's.
So, the Florence scene is the part of a whole ending. We can, of course, argue that all these characters had a massive joint dream, but there are no hints to this (at least I don't see them). Also, the title of the movie is "The Dark Knight Rises", not "falling".
So, I'd say all of that is really happening, along with the scene in Florence cafe.
I am aware that my depiction of the final scenes of the movie is somewhat melodramatic, but I think it was meant to be that way. There are also two things to consider:
When watching it the first time, without spoilers, the viewer was just shocked that the Batman was killed. The whole ending (starting with the uncovering of the Batman's statue) lasts about 3 minutes and 20 seconds. This means that the scenes happen fairly quickly, and the hope/realization part is much more real for the first-time viewer, than for someone reading this.
The context of time when the movie was released. There were plenty of rumors about the movie. I particularly remember the one of Blake possibly being a bad guy (hence the late realization that his legal name is Robin), and that Nolan would kill Bruce (hence the killing, and then the - IMO great - revelation that Bruce did make it).
Last, but not least, it is in the spirit of the movie, and it was announced all along: Bruce had to get free of the Batman and Gotham, and the story is of him rising beyond it all. He (Batman, but necessarily Bruce) is giving it all to these people and, doing so, freeing himself from the misery of Gotham that started by his parent's murder.