The Gariman sector was a region of space.
En route to this sector, during the night shift, the USS Enterprise-D performed with its lateral sensor arrays three separate spectral analyses of the Alwanir Nebula on three distant frequencies. (TNG: "Rightful Heir")
Background information Edit
According to the script, the pronunciation for Gariman was "GARY-man". In the script and at StarTrek.com, Gariman was a star system. The system was in the region of the nebula.
It's unclear if the Enterprise reached the sector before being rerouted to Boreth.
According to the Star Trek: Star Charts, on page 62, the Gariman sector was located in the Beta Quadrant.
The Star Trek Encyclopedia (4th ed., vol. 1, p. 299) identified the Gariman sector as an area of Federation space.