Technically, there is no setting for Paradiso because, in Dante's conception, God's realm is utterly free from time and space. That is the paradox of the poem; Dante is trying to describe in temporal and spatial terms (the only way humans can understand things) something that defies those laws. Basically he's in a timeless nowhere traveling deeper into nowhere. However, this is inherently contradictory because medieval philosophers did indeed think of what we call outer space today as a place. In fact, they saw the universe as geocentric, with the earth in the middle, all the celestial bodies ("stars") revolving around it, and the highest sphere of Heaven at the edges. So, in this sense, at least, there is a spatial setting. For our purposes, we're going to pretend there is a time and space for a setting because this is the only way we humans can understand the book.
So let's take a look at the way Heaven is structured. Like Hell and Purgatory, Heaven has a definite order with nine different layers. Each one is ruled by a "star" (we would call them planets), which is associated with certain human characteristics. These characteristics rub off on the blessed souls found in each sphere and define their flaws and their virtues. For example, the Moon's inhabitants are inconstant because they break their vows, Mercury's inhabitants are motivated by fame, Venus' souls are too passionate, Mars holds warriors, Jupiter houses just rulers, etc. This idea that the environment reflects the inhabitants' moral-state is present in every cantica.
Did you notice that each heaven is called a sphere? Kind of like circles (in Hell and Purgatory), only 3-D? Dante is taking this motif of stacked circular levels and applying it to Heaven. We can envision Heaven the same way we see Hell and Purgatory, if we picture Heaven as a series of circular orbits, which get progressively bigger and bigger the farther away from Earth you go. As in the Inferno, the smaller your circle (your orbit), the more corrupt you are. Earth is the smallest. The Empyrean, or realm of God and the angels, is the largest. Human souls 'inhabit' the "stars" (planets) in between, placed in ascending order of blessedness.
This comes with a caveat. The souls Dante sees in each sphere aren't actually there. How's that for blowing your mind? They only appear in various spheres because this is the only way the human mind can understand their relative blessedness. In reality, they all reside with God up in the Empyrean. He doesn't need to distinguish them by their so-called "stars" because He is all-knowing and can pick out each individual soul seated in his Celestial Rose.
Remember that even the souls are presented differently in Paradiso than elsewhere. Dante cannot actually see them. He cannot say anything about their physical appearances or faces because all he sees are points of light. The idea is that these souls are so much more pure and worthy that Dante cannot even bear to lay eyes on their spiritual brilliance. So, to give you a visual of Paradiso, we can only say that it's basically a lot of little soul-lights surrounded by the larger lights of the stars (planets) themselves. Even Beatrice becomes too bright to look upon when she smiles. So lots and lots of light. No wonder Dante goes blind so often.
There's something fundamentally different about the circles in the first two texts and the orbits in Paradiso. The key lies in the word "orbit." That implies movement, doesn't it? Dante makes it clear to us that the further out from Earth we go, the faster each sphere orbits. The weird thing is that they're orbiting the Earth, which is the center of the universe, but their movement isn't caused by gravity or any attraction to the Earth. Instead, it comes from outside the circle, from the largest, outermost circle of all – the Empyrean. This is where God resides and it is the desire for God that makes each sphere revolve. Naturally, the closer one is to him, the more excited one is, and the faster one moves. This makes Earth a rather sorry story. It is the farthest from God and doesn't move at all (which explains why the circles of Hell and Purgatory are fixed).
Finally, let's talk about time. Dante begins his ascent up the various heavens on noon of Easter Wednesday. Noon is, of course, the brightest time of the day, when the sun shines most directly on the Earth. It may represent Dante's enlightenment after enduring Purgatory. After that, the timeline becomes murkier, which makes sense in the context of Heaven. The whole idea of Paradise is that it is beyond human conception, beyond time and space. We're not sure how long Dante spends in each sphere and when he actually reaches God because we simply cannot grasp the idea of such a journey. For Dante, as for us mortal readers, his journey is timeless.