In "Parallels" a Captain Riker on an Enterprise D from an alternate universes says:
RIKER [on viewscreen]: We won't go back. You don't know what it's like in our universe. The Federation's gone, the Borg is everywhere! We're one of the last ships left. Please, you've got to help us!
It's not so bad in the main alternate universe, but to a lesser degree THE BORG ARE EVERYWHERE!!
Right, left, forward, back, up, down, the Borg are in every direction.
"The Neutral Zone"
DATA: Captain, there is nothing left of Outpost Delta Zero Five.
LAFORGE: Must have been one hell of an explosion.
DATA: Sensors indicate no evidence of conventional attack.
PICARD: Can you determine what happened?
WORF: The outpost was not just destroyed, it's as though some great force just scooped it off the face of the planet.
In "Q who?" Q sends the Enterprise over 7,000 light yeas through space in an unspecified direction.
DATA: According to these coordinates, we have travelled seven thousand light years
[Ten Forward]
DATA [OC]: And are located near the system J two five.
RIKER: Travel time to the nearest starbase?
DATA [OC]: At maximum warp, in two years, seven months, three days, eighteen hours we would reach Starbase one eight five.
Exploring a planet in system J two five they find:
WORF: Captain, the sixth planet in the system is Class M.
DATA: There is a system of roads on this planet, which indicates a highly industrialised civilisation. But where there should be cities there are only great rips in the surface.
WORF: It is as though some great force just scooped all the machine elements off the face of the planet.
DATA: It is identical to what happened to the outposts along the Neutral Zone.
Then the Borg attack and they eventually have to ask Q to save them and send them back to where they were.
In "The Best of Both Worlds":
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Captain's log, Stardate 43989.1. The Enterprise has arrived at Jouret Four in response to a distress signal from one of the Federation's outermost colonies.
[Transporter room]
RIKER: Anything from the surface?
WORF: No sir. There have been no communications from the colony for over twelve hours.
RIKER: Sensors picking up any signs of life?
WORF: None.
O'BRIEN: The surface environment is safe for transport, Commander.
[Planet surface]
RIKER: Mister O'Brien
[Transporter room]
RIKER [OC]: Verify these are accurate coordinates for New Providence colony.
O'BRIEN: Coordinates verified, sir.
[Planet surface]
O'BRIEN [OC]: You're at the centre of town.
(The centre of town is at the edge of a massive crater)
Captain's log, Stardate 43992.6. Admiral Hanson and Lieutenant Commander Shelby of Starfleet Tactical have arrived to review the disappearance of New Providence colony. No sign remains of the nine hundred inhabitants.
[Ready room]
HANSON: The truth is, hell, we are not ready. We've known they were coming for over a year. We've thrown every resource we have into this, but still
RIKER: Then you're convinced it is the Borg?
SHELBY: (blonde woman) That's what I'm here to find out. The initial descriptions of these surface conditions are almost identical to your reports from system J two five.
PICARD: Commander Riker wrote those reports. He agrees with you.
HANSON: We expected much more lead time. Your encounter with the Borg was over seven thousand light years away.
PICARD: If this is the Borg, it would indicate they have a source of power far superior to our own.
HELBY: The soil contains the same magnetic resonance traces That's our footprint. There's no doubt any more. It is the Borg.
Captain's log, stardate 43993.5. With confirmation of the Borg's presence in Federation space, Admiral Hanson has returned to Starbase three two four to discuss strategy with Starfleet Command. Lieutenant Commander Shelby remains on board to continue tactical preparations.
There are Borg at system J25 7,000 light years from Federation space, Borg at the Federation-Romulan Neutral Zone thousands of light years closer to earth, and now Borg in another section of Federation space. These three sets of Borg may belong to one, two, or three different Borg planetary colonies, ships, or fleets.
HANSON [on monitor]: We're coming with every available starship to assist, Captain, but the closest help is six days away.
So the nearest reinforcements are six days away, and no doubt Earth is even farther.
A Borg ship in the area near New Providence attacks the Enterprise, kidnaps Captain Picard, and leaves at warp speed:
WORF: Sir, the coordinates they have set, they're on a direct course to sector zero zero one. The Terran system.
RIKER: Earth.
All during "The Best of Both Worlds Part 2" The Enterprise follows the Borg ship to Earth, and despite being delayed for eight to twelve hours to repair, eventually catch up with it. The Borg ship must travel no faster than The Enterprise and so should not have come from the area near system J25 7,000 light years from Earth but from a closer group of Borg.
As fans remember a federation fleet fights the Borg ship heading straight for Earth at the star system Wolf 359. Wolf 359 is one of the closest stars to earth, being 7.86 light years from Earth.
Wolf 359's coordinates in The equitorial system are right ascension 10 hours 56 minutes 28.99 seconds, declination plus 07 degrees 00 minutes 52.0 seconds.
Converting those coordinates into galactic coordinates using this site:
http://www.robertmartinayers.org/tools/coordinates.html1
Gives the galactic coordinates of 306.5684° 69.8506°.
180 degrees of galactic longitude would be directly opposite the galactic center. 360 degrees would be right back at zero degrees and also pointed at the galactic center.
306.5684 degrees is pointed 53.4316 degrees from the galactic center. Earth is about 25,000 light years from the center of the galaxy and thus from the line separated the Alpha and Beta quadrants from the Gamma and Delta Quadrants.
A line from Earth at 45 degress from the galactic center would intercept the quadrant dividing line 25,000 light years from the galactic center and get farther and farther away from the galactic center as it got farther and farther into the Delta or Gamma Quadrant until it finally left the galactic disc, probably passing outside of Borg space even if it went through the Delta Quadrant and not the Gamma Quadrant.
And a line at 53.4316 degrees from the galactic center would pass through much less of the Gamma or Delta Quadrant than a line at 45 degrees from the Galactic Center.
The galactic latitude of 69.8506° for Wolf 359 is approximately 0.776117 of the 90 degree angle "up" from the galactic equator toward a vertical position "above" Earth. At such a steep angle the Borg ship would have crossed the galactic edge and the galactic barrier only about three to five thousand light years back on it's path - many fans would guess only about a thousand light years back.
if the Borg ship had come straight from the main body of Borg space in the galactic disc about 50,000 light years from Earth, it's trip toward Earth would be angled at a much "lower" galactic latitude.
The Borg already have colonies and fleets and single cubes at least 50,000 light years from the center of Borg space and the usual frontiers of Borg Space, and at least one such group is fairly close to Federation space.
Fortunately most of the Borg groups far from the center of Borg space are very widely and thinly scattered, and don't need to do a lot of assimilating. They spend much time studying each interstellar society or species they encounter, calculating the best time to assimilate it and waiting for decades, centuries, or millennia until they are ready to be harvested by the Borg. But every victim group will have their proper time.
So sooner or later everyone in Federation Space will have reason to sing:
The Borg are back and they're gonna make trouble,
Oh no! oh no! The Borg are Back!
The Borg are back and they're gonna smash Starfleet,
Oh no! oh no! The Borg are Back!
The Borg are back and they're gonna conquer Earth,
Oh no! oh no! The Borg are Back!
The Borg are back and they're gonna assimilate everybody,
Oh no! oh no! The Borg are Back!
THE BORG ARE EVERYWHERE!!