There are two significant repositories of high entropy in the known universe: empty space and black holes.

We can recast the Boltzmann measure of entropy by swapping small sub-volumes of a volume with one another and see if the containing volume changes significantly.

Swapping 1 cm^3 taken from the top of your brain with 1 cm^3 taken from the bottom of your brain will probably cause serious injury or death. Likewise, swapping 1 cm^3 of the valves on the left of your heart with 1 cm^3 of the muscles on the right of your heart will probably kill you. But swapping 1 cm^3 of blood taken from your left leg with 1 cm^3 of blood from your right arm will probably lead to no medical difference at all. So, qualitatively, the heart and brain have higher entropy than blood.

If you take 1 cm^3 of the stuffing of a cushion and swap it with 1 cm^3 of the stuffing elsewhere in the same cushion, you'd struggle to measure a difference by sitting on the cushion.

If you take 1 cm^3 of the air in a room and swap it with 1 cm^3 of the air elsewhere in the room, you'd struggle to notice a difference from outside the room.

And so forth.

We can play with larger volumes: if you are sitting on a cushion in a room, then swapping 1 cm^3 of your blood with 1 cm^3 of air will probably kill you. Swapping 1 cm^3 of a muscle in your leg with 1 cm^3 of the stuffing in the cushion will be unpleasant but not fatal.

In the room, most cm^3 is air rather than brain tissue. If we make the room bigger without adding more people or cushions, we get more air, so a bigger room+cushion+human has lower entropy than a smaller room+cushion+human. Expanding a room in this manner increases its total entropy. Our expanding universe works comparably.

A cm^3 of empty space is to all practical purposes completely substitutable with any other cm^3 of empty space. There's nothing in it. Real space outside galaxy clusters are practically empty, just some photons and neutrinos passing through.

When we consider the metric expansion of space we get two effects: there's more cm^3 of space, but not more photons and neutrinos. Those photons and neutrinos are also cooling, because the expansion is adiabatic.

The expansion of space is generating enormous entropy between clusters of galaxies, and that alone accounts for a large fraction of the increase in entropy in the universe.

Black holes hide what's in them. In a theoretical black hole (and the theory closely matches observation of things that are virtually certainly astrophysical black holes), the no-hair conjecture says that apart from position in and motion through spacetime, which we can remove by using a set of coordinates in which the (theoretical) black hole's mass M is always at the spatial origin, the only measurable values in electrovacuum are electric charge, angular momentum, and mass. What makes up M or contributes to the angular momentum or charge is unknown just by looking at a black hole at any given moment.

We can probe this a bit. Let's say our "snapshot" black hole's charge is completely neutral. Is that because only neutral charges have ever fallen into it? Or because a mix of opposite charges have fallen in over time, neutralizing small deviations in charge away from 0? We don't know. Same with angular momentum. We also don't know what things combined to give us the mass M.

In fact, consider a chargeless nonspinning spherically symmetrical black hole of mass M. We can raise M a small amount i by throwing in a thin collapsing shell of gas of mass ~ i. Or we can throw in two thin collapsing spherically-symmetrical shells of gas where each has mass ~ i/2. Or we can throw in three thin collapsing spherically-symmetrical shells of gas each of mass ~ i/3. And so on. A future observer would not know -- thanks to no hair -- the count of shells we threw in: it would only see a new black hole with one observable: M' where M' > M.

Because we can substitute the "insides" of a black hole arbitrarily as long as we preserve its observable quantities, a no-hair black hole can have absolutely enormous entropy. Additionally, a black hole with a larger mass has more entropy than a black hole with a smaller mass.

Astrophysical black holes probably only grow (and if they ever evaporate by the Hawking process then they mostly emit greybody radiation, which is extremely high entropy). Moreover, they grow by intercepting lower-entropy material, whether that's stars, molecular clouds, distant starshine, or the cosmic microwave background, all of which is of lower entropy.

Assuming the black holes that one finds in galaxy clusters tend to merge (which raises their entropy), and the metric expansion of space continues indefinitely, the far future of the universe is very large black holes surrounded by enormous amounts of space containing an increasingly sparse, increasingly cold gas of material that managed to avoid being stuck in galaxy clusters in the earlier universe which still had lower-entropy structures like stars and planets.

We can look backwards too: when we reverse the metric expansion of space, galaxy clusters are closer together, and the cosmic microwave background and the like gets denser and hotter. Stellar black holes become less numerous; central black holes in clusters and galaxies are smaller. Thanks to light being pretty slow (and also gravitational lensing) we can test this by probing "first light", "the dark ages", and other epochs that are accessible to conceivable observatories. It would be a super-interesting discovery to see more black holes in more distant (and thus older) galaxies than in closer ones, for instance, because it would directly implicate questions about the total entropy of the universe. Likewise, when we study the metric expansion of space there perhaps we could (shockingly) discover that remote "empty space" has much lower entropy than expected. These aren't very likely, though: it's safer to bet on the total entropy of the universe growing for a very very very long time thanks to the metric expansion of space outside galaxy clusters, and the gravitational collapse of matter inside galaxy clusters.