Nowhere ... or Everywhere; The Halls of the Dead
It is never explained what lies beyond the portal. It is heavily implied that there is unknown machinery directly behind the yellow and black painted door that is somehow supporting the beam.
The closest we get
is Roland's guess that they lead to somewhere "Beyond ka"
"When everything was new, the Great Old Ones -- they weren't gods, but people who had almost the knowledge of gods -- created Twelve Guardians to stand watch at the twelve portals which lead in and out of the world ..."
...
"Portals," Eddie mused. "Doors, you mean. We're back to those again. Do these doors that lead in and out of the world open on the world Suze and I came from? Like the ones we found along the beach?"
"I don't know," Roland said.
...
"Well, make a guess!" Eddie exclaimed
...
"Not true -- sometimes the man does [make a guess]," Roland said, surprising them both. "When guessing's the only thing left, sometimes he does. The answer is no. I don't think -- I don't guess -- that these portals are much like the doors on the beach. I don't guess they go to a where or when that we would recognize. I think the doors on the beach -- the ones that led into the world that you both came from -- were like the pivot at the center of a child's teeterboard."
...
"Yes. On one end, my ka. On the other, that of the man in black -- Walter. The doors were the center, creations of the tension between two opposing destinies. These other portals are things far greater than Walter, or me, or the little fellowship we three have made."
"Are you saying," Susannah asked hesitantly, "that the portals where these Guardians stand watch are outside ka? Beyond ka?"
"I'm saying that I believe so," He offered his own brief smile, a thin sickle in the firelight. "That I guess so."
-- King, S. (2003). Bear and Bone. The Wastelands: The Dark Tower III. New York: A Signet Book.
As well as a little later on, Roland's admission that he doesn't know.
"So this is one of the twelve portals. Where does it go, Roland? Disney World?"
Roland shook his head. "I don't know where it goes. Maybe nowhere ... or everywhere. There's a lot about my world I don't know -- surely you both have realized that. And there are things I used to know which have changed."
-- King, S. (2003). Bear and Bone. The Wastelands: The Dark Tower III. New York: A Signet Book.
The sound of machinery
is described when Roland and Eddie are first approaching the clearing where the bear lived
The sounds were louder now, and he [Eddie] began to sort them out. One was a low, deep, humming noise. He could feel it in his feet -- a faint vibration, as if some large piece of machinery was running in the earth. Above it, closer and more urgent, were crisscrossing sounds like bright scratches -- squeals, squeaks, chitterings.
...
On their side of the stream, backed up against the wall, was a metal box about nine feet high. Its roof was curved, and it reminded Eddie of a subway entrance.
-- King, S. (2003). Bear and Bone. The Wastelands: The Dark Tower III. New York: A Signet Book.
But there is something that reminds Eddie
of the house in Dutch Hill from his where.
As Eddie approached the metal box with its alternating diagonal slashes of yellow and black, a strong and unpleasant memory sized him -- for the first time in years he found himself thinking of a crumbling Victorian wreck in Dutch Hill, about a mile away from the neighborhood he and Henry had grown up.
...
He felt that same old sense of mystery and danger now, as he approached the metal box. Gooseflesh began to ripple up his legs and down his arms; the hair on the back of his neck bushed out and became rough, overlapping hackles. He felt that same subtle wind blowing past him, although the leaves on the trees which ringed the clearing were perfectly still.
Yet he walked toward the door anyway (for that was what it was, of course, another door, although this one was locked and always would be against the likes of him), not stopping until his ear was pressed against it.
It was as if he had dropped a tab of really strong acid half an hour ago and it was just beginning to come on heavy. Strange colors flowed across the darkness behind his eyeballs. He seemed to hear voices murmuring up to him from long hallways like stone throats, halls which were lit with guttering electric torches. Once these flambeaux of the modern age had thrown a bright glare across everything, but now they were only sullen cores of blue light. He sensed emptiness … desertion … desolation … death.
…
“All is silent in the halls of the dead,” Eddie heard himself whisper in a falling, fainting voice. "All is forgotten in the stone halls of the dead. Behold the stairways which stand in darkness; behold the rooms of ruin. These are the halls of the dead where the spiders spin and the great circuits fall quiet, one by one.”
Roland pulled him roughly back, and Eddie looked at him with dazed eyes.
-- King, S. (2003). Bear and Bone. The Wastelands: The Dark Tower III. New York: A Signet Book.