Section I, Lines 21-25 Summary

Get out the microscope, because we’re going through this poem line-by-line.

suffering Eastern sweats and Tangerian bone-grindings and migraines of China under junk-withdrawal in Newark's bleak furnished room,

We're still trying to figure out where these folks went.
Maybe they have gone East, that is, to Asia. Or perhaps Tangiers, in northern Morocco.
Or maybe just Newark, New Jersey, where they suffer from "junk-withdrawal," a painful condition caused by suddenly stopping drug use. Once again, the New Jersey option seems most likely, though Ginsberg wants to suggest that the physical ailments suffered by people who quit using drugs are a form of world travel.

who wandered around and around at midnight in the railroad yard wondering where to go, and went, leaving no broken hearts,

They seem to have a lot of free time on their hands. Here they wandered around a railroad yard and then left without anyone missing them that much.

who lit cigarettes in boxcars boxcars boxcars racketing through snow toward lonesome farms in grandfather night,

The "best minds" also include homeless people who travel illegally on freight trains.
They smoked in several of the train's boxcars as they travel out to the countryside.
They may or may not have any family remaining, but the night is like their "grandfather."

who studied Plotinus Poe St. John of the Cross telepathy and bop kabbalah because the cosmos instinctively vibrated at their feet in Kansas,

In some ways, these "minds" are conventionally smart. They have studied Plotinus, a philosopher who lived in the time of the Roman Empire, also Edgar Allan Poe, the 19th century American writer, and St. John of the Cross, a religious mystic.
In addition to these scholarly topics, their studies include "telepathy," or mind-reading, and "bop kabbalah," which Ginsberg just made up out of the blue by combining "bop," meaning jazz, and "kabbalah," a school of Jewish mysticism.
Why did they study these things? Because "the cosmos instinctively vibrated at their feet in Kansas."
The overall point is that they tend to be interested in dense philosophy and various forms of religious mysticism. A "mystic" is someone who hopes to achieve revelations into the ultimate nature of things.

who loned it through the streets of Idaho seeking visionary indian angels who were visionary indian angels,

They traveled alone through towns in Idaho looking for "visionary Indian angels," or Native Americans with sacred powers.
They may or may not have been "visionary Indian angels" themselves.