Did Jesus and his disciples have an occasional “hiding place”? We see at Jn 11:6, the immediate response of Jesus to the news that Lazarus was seriously ill:

... after having heard that Lazarus was ill, he stayed two days
longer in the place where he was.

Going back to Jn 10:39-40,  we see where Jesus was at that time:

Then they tried to arrest him again, but he escaped from their hands.
He went away again across the Jordan to the place where John had been
baptizing earlier, and he remained there.

It is traditionally believed that the location of the Al-Maghtas ruins on the eastern side of the Jordan River was where Jesus was baptized and where John the Baptist ministered.
Jesus says elsewhere:

Foxes have dens and birds have nests, but the Son of Man has no place
to lay his head.” (Lk 9:58).

That remark perhaps alludes to the itinerant nature of his public life, though he had his mother and a house in which she lived.
Now, Jesus was widely believed to be preparing for the establishment of an earthly kingdom. Naturally, he and his disciples were in the watch-list of the Roman authorities, with some Jews more than eager to betray the group. It was therefore only natural for Jesus and his disciples to stay out of public gaze, at least on certain occasions, such as the time of Lazarus's illness.
The Ruins across Jordan appear to be qualifying for such a hiding place. Of course, the Gospels do not explicitly name any place where Jesus and his disciples spent time away from public view.
My question therefore is: Did Jesus and his disciples have an occasional 'hiding place'? Views of any denomination are welcome.
You may have answered your question with your own statement:

Of course, the Gospels do not explicitly name any place where Jesus and his disciples spent time away from public view.

Had the Holy Spirit wanted the gospel writers to include the name of such a hiding place, he would have inspired them to name it. Since the Spirit did not, however, no such place is mentioned, at least explicitly.
What the Gospels do mention explicitly is that--as you have pointed out--Jesus frequently needed to escape public notice by making himself scarce! His reason for doing this is linked intimately to his life's timetable.
At Cana in Galilee, the place of Jesus's first public miracle, Jesus said to his mother,

&quot;Woman, why do you involve me?&quot; Jesus replied. “My hour has not yet come” (John 2:4 NIV).

The phrase &quot;my hour has not yet come&quot; is significant. Commentator Constable has this to say regarding Jesus's words &quot;my hour&quot;:

The Greek word translated time (ὥρα, hōra) occurs in John 2:4; 4:21, 23; 5:25, 28, 29; 7:30; 8:20; 12:23, 27; 13:1; 16:25; and 17:1. It is a reference to the special period in Jesus’ life when he was to leave this world and return to the Father (13:1); the hour when the Son of man is glorified (17:1). This is accomplished through his suffering, death, resurrection (and ascension—though this last is not emphasized by John). John 7:30 and 8:20 imply that Jesus’ arrest and death are included. John 12:23 and 17:1, referring to the glorification of the Son, imply that the resurrection and ascension are included as part of the “hour.” In John 2:4 Jesus’ remark to his mother indicates that the time for this self-manifestation has not yet arrived; his identity as Messiah is not yet to be publicly revealed.

In saying &quot;my hour has not yet come,&quot; Jesus was indicating the importance he placed on doing his Father's will, and that included the when, the where, the how, and the why. Jesus said,

. . . I do nothing on my own but speak just what the Father has taught me. The one who sent me is with me; he has not left me alone, for I always do what pleases him” (John 8:28b-29 NIV).

Saying and doing what pleased the Father was Jesus's priority. Equally important to Jesus was being sensitive to when and what the Father wanted him to do and say. Again, the Father's timetable was Jesus's timetable. If saying or doing something would in any way jeopardize its timely fulfillment, Jesus would immediately adjust his course accordingly. Sometimes that adjustment involved making himself (and his disciples) hard to find.
In short, Jesus may have had numerous hiding places during his public ministry. Since the Gospels do not mention explicitly where those places were, save in general terms such as &quot;across the Jordan,&quot; we must assume the Spirit who inspired the Gospel writers chose not to bring those locations to their minds as they wrote.
By the way, the disciples had a hiding place where they could lay low after Jesus's crucifixion. &quot;For fear of the Jews&quot; they were behind locked doors. Perhaps this location was where Jesus and his disciples celebrated the Last Supper together. Just a thought!