It’s entirely possible that dreamers simply don’t go anywhere.
Dream has never been a major part of the Great Wheel cosmology—it’s only been mentioned in five publications:
- Guide to the Ethereal Plane where it is very little more than a mention.
- Ravenloft adventure The Nightmare Lands which includes rules for adventuring in dreamscapes. Guide to the Ethereal Plane explicitly directs you here if you want to actually go to Dream.
- Manual of the Planes, by far the most detailed version. It still isn’t very.
- Dragon vol. 287, “Dreamlands: Variant Planes of Dream” which doesn’t actually discuss Dream per se, but rather other ways you could implement different kinds of planes for dreaming: inner plane, outer plane, transitive plane, individualized demiplanes for each dreamer, etc.
- Manual of the Planes, which has a few paragraphs on it.
There is no 5th-edition Manual of the Planes (yet?), so the most likely place to expect to find information on Dream doesn’t exist. Mordenkainen’s Tome of Foes has been the only real source we have so far on planar matters, but it’s devoted pretty heavily to, ya know, “foes,” and Dream doesn’t provide a lot of those, particularly not many that are easily included in a regular campaign.
Notably, 1e and for a good while 2e had the Great Wheel (even if it wasn’t named that yet for 1e) without any mention of Dream, and the 3.5e “revision” of Manual of the Planes, Planar Handbook, didn’t bother to mention it either. Outside of those five publications, the entire concept never got used in any way, and even if it was supposed to officially exist somehow, it was ignored.
Thus, for the most part, the Great Wheel doesn’t bother with Dream. You can use the write-ups from 2e or 3e or even 4e (though that was the “World Axis” nonsense, not the Great Wheel) if you want, but even those editions themselves mostly elected to simply not, and it’s quite likely that 5e is going to follow that pattern—even if it does get mentioned in an eventual Manual of the Planes or similar, it’s quite likely to be something that never gets mentioned or leveraged again after that.
Dal Quor, Eberron’s Moon/Plane of Dreams
The exception to all this is Eberron, where Dal Quor is a major part of the setting. That said, if Eberron is connected to the Great Wheel—which is itself debatable—how is completely unknown and a matter of guesswork and speculation. Dal Quor is extremely important to Eberron, but almost certainly irrelevant everywhere else. It is extremely unlikely that dreamers from other worlds go to Dal Quor, unless Dal Quor somehow is Dream (at least in previous editions, the descriptions of the two would have made that quite difficult to reconcile, however).