In their two decades of incursions in the Alpha Quadrant, the Borg seem to have focused their attentions on the Federation, and on the Federation's central world of Earth. This makes sense, even for reasons unrelated to Borg origins: the Federation was the largest political entity in the area, and its technology was at very worst on par with the regional average, more likely somewhat above.
The TV series did suggest that the Borg had an interest in other powers, though. The Neutral Zone outpost scoopings were as much on the Romulan side of that frontier as on the Federation side, and the Klingons had apparently sent warships to Wolf 359. Outside of the TV series, Ruriko Tenmei (and several dozen others) were lost preventing the Borg's assimilation of Cardassian Krem Varuda's AI in 2369, the "Operation Assimilation" comic from 1997 showed the Borg's 2364 Neutral Zone incursion from the Romulan perspective, and the Strange New World
story "Suicide Note" suggested Alidar Jarok defected substantially because he and his allies were very concerned by reports of the Borg obtained from Romulan probes deep in the Beta Quadrant.
Are there any other notable encounters between the Borg and the Federation's neighbours in Treklit?